The magnitude of the cross product:

$\overline{){\mathbf{|}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{A}}{\mathbf{\times}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}{\mathbf{|}}{\mathbf{=}}{\mathbf{\left|}}{\mathbf{A}}{\mathbf{\right|}}{\mathbf{\left|}}{\mathbf{B}}{\mathbf{\right|}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta}}}$

Cross product:

$\overline{)\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}{\mathbf{\times}}\stackrel{\mathbf{\rightharpoonup}}{\mathit{B}}{\mathbf{=}}{\mathbf{(}}{{\mathit{A}}}_{{\mathit{y}}}{{\mathit{B}}}_{{\mathit{z}}}{\mathbf{-}}{{\mathit{A}}}_{{\mathit{z}}}{{\mathit{B}}}_{{\mathit{y}}}{\mathbf{)}}{\mathbf{}}\hat{\mathbf{i}}{\mathbf{+}}{\mathbf{(}}{{\mathit{A}}}_{{\mathit{z}}}{{\mathit{B}}}_{{\mathit{x}}}{\mathbf{-}}{{\mathit{A}}}_{{\mathit{x}}}{{\mathit{B}}}_{{\mathit{z}}}{\mathbf{)}}{\mathbf{}}\hat{\mathbf{j}}{\mathbf{+}}{\mathbf{(}}{{\mathit{A}}}_{{\mathit{x}}}{{\mathit{B}}}_{{\mathit{y}}}{\mathbf{-}}{{\mathit{A}}}_{{\mathit{y}}}{{\mathit{B}}}_{{\mathit{x}}}{\mathbf{)}}{\mathbf{}}\hat{\mathbf{k}}}$

**Part A**

|A×B| = (6)(4)sin(180°- 45°) = 17

The magnitude of the cross product A×B is 17.

Evaluate the cross products A×B and C×D? (Figure 1)

Part A

What is the magnitude of the cross product A×B? Express you answer using two significant figures.

Part B

What is the direction of the cross product A×B? (multiple choice)

a) into the plane of the image

b) it is opposite to the direction of A

c) out of the plane of the image

d) A×B is zero vector

e) it is opposite to the direction of B

Part C

What is the magnitude of the cross product C×D?

Part D

What is the direction of the cross product C×D? (multiple choice)

a) it is opposite to the direction of C

b) C×D is zero vector

c) into the plane of the image

d) it is the opposite to the direction of D

e) out of the plane of the image

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Cross Product (Vector Product) concept. If you need more Intro to Cross Product (Vector Product) practice, you can also practice Intro to Cross Product (Vector Product) practice problems.