Vectors

Question 1

What is the dot product of vector u and vector v?

Answer 1

u.v = |u| * |v| cosθ

Question 2

What is the dot product of vector u and vector v if they are perpendicular?

Answer 2

0

Question 3

What is the cross product of vector u and vector v?

Answer 3

u x v = |u| * |v| sinθ

u x v is perpendicular to u and v

Question 4

What is the cross product of vector u and vector v if they have the same direction?

Answer 4

0

Question 5

What does | u x v | represent geometrically?

Answer 5

The area of a parallelogram with edge vector u and v.

Question 6

What is one way of obtaining the direction of the vector product?

Answer 6

The right hand rule.

Question 7

What is one application of the cross-product?

Answer 7

M = r x F

Question 8

What is one application of the dot product?

Answer 8

W = F.v

Question 9

What is the scalar triple product of vectors?

Answer 9

u.(v x w)

This is calculated as a 3x3 determinant.

Question 10

What does | u.(v x w) | represent geometrically?

Answer 10

The volume of the parallelepiped with the 3 vectors as edge vectors.

Question 11

When are the vectors u, v and w linearly independent?

Answer 11

Iff their scalar triple product ~= 0.