Vectors and Forces

Question 1

What is a scalar quantity?

Answer 1

It’s a quantity with a magnitude but no direction.

Question 2

What is a vector quantity?

Answer 2

It’s a quantity with a magnitude and direction.

Question 3

How do you turn a vector into a unit vector?

Answer 3

u = a / |a|

Question 4

What is the Scalar Product of the two vectors a and b?

Answer 4

a . b = |a| |b| cos(x) where x is the angle between the two vectors
We can also multiply the x, y, and z components for each component, and then we can sum the values

Question 5

What is the Vector Product of the two vectors a and b?

Answer 5

It is the cross product (Put it in a matrix, and calculate the derivatives for the minor matrices along the axis)

Question 6

What is the moment of a force about a point?

Answer 6

The moment of a force about a point is, by definition, the vector (cross) product between the position vector of the origin of the force and the force itself