Vectors First Unit

Question 1

What value makes said set collinear

Answer 1

x1/x2=y1/y2=z1/z2

Question 2

What value makes components perpendicular

Answer 2

Make the dot product = 0

Question 3

a-b or a+b

Answer 3

Subtract components or add if addition

Draw with said angle and use cosine law to find

Question 4

Finding magnitude of vector

Answer 4

Use pythagoras

Question 5

Find angle between two vectors

Answer 5

Dot product, then find magnitudes, then plug into formula of cosΘ = u dot v/ |u|*|v|

Question 6

Airplane heading in y and x direction, find resultant velocity

Answer 6

If asks for how far in said time, use cosine law and then multiply by time

For direction, use angle to form with x axis

For angle make a parallelogram and then find the outside angle of the first direction

Question 7

Components for unit vector perpendicular

Answer 7

Cross product, find magnitude, divide each component by magnitude

Question 8

Find area of the triangle of the triangle when given vertices

Answer 8

Find AB components and AC components, then AB x AC, then ½ of pythagoras formula

Question 9

Vectors a, b,c form a parallelepiped, find the volume.

Answer 9

|a dot (b x c)| → absolute value not magnitude

Question 10

Projection (v onto u)

Answer 10

= (v dot u/|u|^2)*u (answer should be in component form)

Question 11

A force of said magnitude acts in the direction of said vector and moves an object from point A to point B, find work done.

Answer 11

ending components - beginning components, gives you displacement and then find magnitude of displacement

for angle find dot product of said vector and displacement and make it equal to magnitude of said vector * magnitude of displacement * cosΘ, and rearrange for Θ

Question 12

Find the projection onto each axis

Answer 12

For x axis use (1,0,0), for y use (0,1,0), for z use (0,0,1) as other vector with given vector

Question 13

Vertical and horizontal components formula

Answer 13

Fv = |F|sinΘ and Fh = |F|cosΘ