







Espaces vectoriels 
20020818 

Bacar pose la question : Comment montrer que trois (ou plus que trois) sous espaces vectoriels sont en somme directe. Claude Tardif lui répond. 





Vectors 
20190906 

Kayla pose la question : Hi!
Due to time constraint issues, we skipped vectors in PreCalc last year. However, I'm attempting to complete my AP Physics summer homework and there are 3 problems with vectors. As I explained, I have no idea even where to begin and as such I need some help.
Problem 1:
A plane flying at 90° at 45 m/s is blown toward 0° at 62 m/s by a strong wind. Find the plane's resultant velocity.
I have tried all sorts of online calculators but none are providing me with a formula I can use to solve this problem on my own.
Problem 2:
If you walk 367 m North and 785 m West what is your total displacement from your original location?
What is the problem asking for when it says displacement?
Problem 3:
A plane travels on a heading of 127.0° at a velocity of 25 km/hr. What are the horizontal and vertical components of the plane's velocity?
As you know already, I have never done vectors so I don't know what horizontal and vertical components of velocity are.
Thank you So Much for your help!! I am struggling!!
 Kayla Penny Nom lui répond. 





A range hood 
20171204 

Chuck pose la question : I'm building a custom range hood and can't seem to get the angles correct where the front and side panels intersect.
I saw a similar post but there's no way I can do the calculations for a Wolfram Alpha!
Here are the dimensions that I have (in inches)...
Base  Front 29 7/16" x side 19 3/16"
Top  Front 10" x side 9"
Front Panel Length (from base to top on an angle) 21"
Side Panel Length (from base to top on an angle)  17 9/16"
Vertical distance from the base to the top 14 1/4 inches.
Any help finding the bevel/miter of the two front corners where the sides meet the front panel would be greatly appreciated.
I will need the angle for the saw in degrees.
Thank you in advance!
Regards,
Chuck Harley Weston lui répond. 





The angle between two planes 
20170912 

Arthi pose la question : Hello. hope you are having a good day.
I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism.
How can I do this?
Please reply as soon as possible
Thank You Penny Nom lui répond. 





Speed and velocity 
20160214 

kechi pose la question : A boat sails south through Chesapeake Bay. It takes 10 hours to sail 110 kilometers. Describe the boat's motion. Calculate the boat's speed and velocity, showing the calculations. Explain how the boat's speed is different from its velocity Penny Nom lui répond. 





The line of intersection of two planes 
20151209 

Rabz pose la question : Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Penny Nom lui répond. 





Column vectors 
20150221 

jill pose la question : A has co ordinates (7,1) and B has coordinates (3,5).write these as column vectors Penny Nom lui répond. 





Vector division 
20120828 

Nazrul pose la question : If A and B be two vectors where B = 3 A The What is B/A ?
Please help me. Robert Dawson lui répond. 





Building a custom range hood 
20111008 

Bill pose la question : I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Harley Weston lui répond. 





The length of a vector 
20100912 

kyrie pose la question : Find the possible values of the constant a such that
 ai + 4aj + 4k  = 13
I know the answer is 3 but not sure how to get to it Penny Nom lui répond. 





Two non zero vectors 
20091027 

Nazrul pose la question : Given that a and b are two non zero vectors and ma+nb=0 where m and n are two scalars. How can I prove that m=n=0. Robert Dawson lui répond. 





An aeroplane flying in a wind 
20090602 

Maria pose la question : The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air,
are such that its resultant speed and direction are 800 kph, and direction N71.6◦E
I need to find the size of the angle between v and vw, in degrees to one
decimal place, and find the speed at which the aeroplane would fly if the air were
still, to the nearest kph.
It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane
would have if the air were still, the velocity vw of the wind, and
the resultant velocity v of the aeroplane (diagram should be
in the form of a triangle illustrating how one velocity vector is the
sum of the other two)
Thanks Harley Weston lui répond. 





The midpoints of two sides of a triangle 
20090317 

Manis pose la question : Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Robert Dawson lui répond. 





Find the resultant of this displacement pair 
20090222 

katydidit pose la question : Find the resultant of this displacement pair:
500 miles at 75 degrees east of north and
1500 miles at 20 degrees west of south.
How do I graph this and how do I solve this problem? Penny Nom lui répond. 





The path of a small sailboat 
20081119 

jane pose la question : a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East
then 3.40 km North East, then an additional distance in an unknown direction. Her final position
is 6.68 km directly east of the starting point. find the magnitude & direction
of the third leg of the voyage. Harley Weston lui répond. 





Vectors and an orientation change in the axes 
20080830 

moumita pose la question : what differences take place to a vector because of choice of orientation of the coordinate axes and why?? Harley Weston lui répond. 





A roof angle 
20080830 

carla pose la question : Use vectors to find the angle in the attached diagram Chris Fisher and Stephen La Rocque lui répond. 





The flight of an airplane 
20080829 

kobina pose la question : You are traveling on an airplane that is moving at 500 mph in a direction 40deg north of west.Therefore , You are travelling (due to the plane ) at how many mph toward the west. Stephen La Rocque lui répond. 





A force vector 
20080828 

moumita pose la question : F=20N...this force is acting along a vector A=4j+3k.what is F? Penny Nom lui répond. 





Two forces acting on a body 
20080621 

Rita pose la question : Before answering the question below, what exactly is, in basic words, resultant force?
QUESTION:
Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds.
Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force. Harley Weston lui répond. 





Scalar triple product and volume of a general tetrahedron 
20070803 

Anurag pose la question : how do you prove that
volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c? Stephen La Rocque lui répond. 





The bearings of a ship's journey 
20070720 

sugar pose la question : A ship starts from point osail eastward for 6 hours. Then changes its course to N50E for 8 hours and then N62W for 10 hours until it reaches the point c. If the speed of the ship was imi/h, what is the bearing of the side oc? Harley Weston lui répond. 





The velocity of an aircraft 
20070322 

William pose la question : Hello,
I don't understand how to work this problem. Thanks in advance for your help!
A jet moving at 500.0 km/h due east moves into a region where the wind is blowing at 120.0 km/h in a direction 30.0 degrees north of east. What is the new velocity and direction of the aircraft relative to the ground? Penny Nom lui répond. 





vectors 
20070225 

harsh pose la question : Two vectors U= Uxi 6j +k And V= 3i +Vyj +k. Their dot product U.V= 35. AND the magnitude of their sum is U+v= 3. What are the components of Ux and Vy ? Stephen La Rocque lui répond. 





Romeo is throwing pebbles 
20070208 

Jessie pose la question : Romeo is chucking pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall. How fast are the pebbles going when they hit her window? Stephen La Rocque lui répond. 





An octagonal bird house 
20070113 

Soren pose la question : I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew! Harley Weston lui répond. 





Bearings 
20061122 

Suzy pose la question : Mr. John wants to fly her airplane from point A to B, a distance of 450 miles. If B has a heading of 60 degrees from A, and there is a constant wind from the southeast blowing at 60 mph, find the speed and heading she should maintain in order to land at B in 90 minutes. Stephen La Rocque lui répond. 





Equations of two lines 
20060405 

Wael pose la question : Determine a cartesian equation of the line passing through A and V as a direction vector?
1 A (2;1) and V = j
2 A (2;3) and V = i Penny Nom lui répond. 





Find the ground speed and the planes true heading. 
20060205 

Jimmie pose la question : An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading. Penny Nom lui répond. 





The combined force of two vectors 
20041030 

Brian pose la question : Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + 5j, and the other team exerts a force represented by the vector b = 8i3j.
1.Determine the direction of movement of the ball if the i axis is due east.
2.Determine the combined force magnitude. Harley Weston lui répond. 





Vectors in three space 
20041030 

Jo pose la question : I have two questions that I just cannot visulise and dont know how to get started on them..!
1. Ship X is sailing North at 4m/s and Ship Y is sailing due East at 3m/s. A sailor on Ship X climbs a vertical pole at 1/2 m/s. What is the velocity of the sailor on Ship X relative to an observer on Ship Y? State it's magnitude and direction.
Not sure where to start with this one...
2. Show, using vectors, that for any tetrahedron, the segments joining the midpoints of the opposite edges are concurrent.
i know what a tetradedron is, and what I am proving but do I solve simultaneously for a specific case?? Walter Whiteley lui répond. 





The force of a 5000 tonne lorry 
20041027 

Aaron pose la question : A 50 tonne lorry is parked on a slope with a gradient of 4%.
Due to the self weight of the lorry, what is the force
* acting down the slope
* acting normal (at right angles) to the slope Penny Nom lui répond. 





An aircraft is flying directly from airport A to airport B 
20041022 

A student pose la question : In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i30j)km/h. Calculate
(i) the time of flight, to the nearest min
(ii) the direction of the wind. Penny Nom lui répond. 





Cycling in the wind 
20041011 

A student pose la question : A cyclist is travelling in the direction of 12i+5j at a speed of 39 km/h where i is a unit vector due east and j is a unit vector due north. The wind appears to the cyclist to be blowing with a velocity of (4i+j) km/h. Find, correct to 1 d.p
(a) the true speed of the wind and
(b) the bearing from which the wind is blowing
Penny Nom lui répond. 





A parallelepiped 
20040925 

Aman pose la question : " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,2), B is (3,6,1), and C is (4,0,1), find the coordinates of the other vertices of the parallelepiped.)" Penny Nom lui répond. 





Two vector problems 
20040714 

Jaye pose la question : Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Penny Nom lui répond. 





The commuter 
20040714 

JJ pose la question : A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time.
Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Penny Nom lui répond. 





Vectors 
20040706 

Annie pose la question : a=3ij+2k and b=i+3j2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k. Chris Fisher lui répond. 





Arc length 
20020417 

Vix pose la question : Find the point on the curve r(t)=(12sint)i(12cost)j+5tk at a distance 13pi units along the curve from the point (0,12,0) when t=0 in the direction opposite to the direction of increasing arc length. Harley Weston lui répond. 





Translated by the vector (5,2) 
20011119 

Jennifer pose la question : Give the image of (p,q) when translated by the vector (5,2). Penny Nom lui répond. 





Multiplying vectors 
20011022 

Murray pose la question : Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Harley Weston lui répond. 





The speed of the boat 
20010712 

Sharon pose la question : A motor boat is travelling in a southeasterly direction in water that is flowing from the south at 2km per hour. Show that the speed of the boat is (6 times the square root of 2) km per hour, given that it can travel at 10km per hour in still water. Penny Nom lui répond. 





The angle of rotation 
20000803 

Jay pose la question : I have the following information Given. (X1, Y1) Origional Point (X2, Y2) Origional Point After a Rotation (Xa, Xb) Center of Rotation What formula would I use to figure out the angle the point was rotated? Chris Fisher and Harley Weston lui répond. 





Area of a triangle from vertex coordinates 
19990421 

Mark Tyler pose la question : I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too. I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula: A = abs((x1x2)*(y1y3)(y1y2)*(x1x3)) for triangle (x1,y1)(x2,y2)(x3,y3) I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long. Regardless, it may be fun for the kids, even if it's not on the curriculum. Walter Whitley lui répond. 





Finding the Mine 
19970623 

Billy Law pose la question : Tom is gold prospector. On his last trip out from town, he headed 35 degree South of West to a lake where he had lunch. The lake was 24 km out of Town. He then headed due East for 35 km before Doubling back on bearing of 15 degree South of west for 20 km to reach his mine. By converting to Cartesian coordinate before doing vector additions do the following: a) Calculate the position of the mine from town in term of a distance and a direction. ... Harley Weston lui répond. 

