Problem: Evaluate the cross products A×B  and C×D? (Figure 1)Part AWhat is the magnitude of the cross product A×B? Express you answer using two significant figures.Part BWhat is the direction of the cross product A×B? (multiple choice)a) into the plane of the imageb) it is opposite to the direction of Ac) out of the plane of the imaged) A×B is zero vectore) it is opposite to the direction of BPart CWhat is the magnitude of the cross product C×D?Part DWhat is the direction of the cross product C×D? (multiple choice)a) it is opposite to the direction of Cb) C×D is zero vectorc) into the plane of the imaged) it is the opposite to the direction of De) out of the plane of the image

FREE Expert Solution

The magnitude of the cross product:

$\overline{){\mathbf{|}}\stackrel{\mathbf{⇀}}{\mathbf{A}}{\mathbf{×}}\stackrel{\mathbf{⇀}}{\mathbf{B}}{\mathbf{|}}{\mathbf{=}}{\mathbf{|}}{\mathbf{A}}{\mathbf{|}}{\mathbf{|}}{\mathbf{B}}{\mathbf{|}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta }}}$

Cross product:

Part A

|A×B| = (6)(4)sin(180°- 45°) = 17

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

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Problem Details

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