Vectors

Question 1

What is a vector? What is a scalar?

Answer 1

A vector has both magnitude & direction; a scalar only has magnitude, no direction.

Question 2

Distance is —? Displacement is __?

Answer 2

Distance is a scalar & the total length traveled.

Displacement is a vector & is always a straight arrow

Question 3

What are the x- and y-components of a vector equal to?

Answer 3

x-component:
Ax = |A|cosθ

y-component:
Ay = |A|sinθ

Question 4

What is the formula for the magnitude of a resultant vector?

Answer 4

|R| = √(A)^2 + (B)^2

Question 5

The unit vectors: i, j, k correspond to what axises on a 3D coordinate plane?

Answer 5

i = x-axis
j = y-axis
k = z-axis

Question 6

What is the formula for the direction of the resultant vector?

Answer 6

θ = Arctan (opp. / hyp.)

or

θ = Arctan (y component / x component)

Question 7

Does a vertical vector have an x-component?

Does horizontal vector have a y-component?

Answer 7

No.

A vertical vector only has a y-component (it’s x=0).

A horizontal vector only has an x-component (it’s y=0).

Question 8

What should you immediately do when you have a vector involving an angle?

Answer 8

Break it down into its components!!

Question 9

What is the formula for the dot product?

Answer 9

A•B = |A||B|cos θ

or

A•B = AxBx + AyBy

Question 10

What is the formula for the cross product?

Answer 10

AxB = |A||B|sin θ