First slide

Vectors

Question

If $\vec{A} \times \vec{B} = \vec{C}$ , then

Moderate

A

$\vec{A} . \vec{B}$ must be zero
B

$\vec{C} . \vec{A}$ may be zero
C

$\vec{C} . \vec{B}$ may be zero
D

$\vec{C} . (\vec{A} + \vec{B})$ must be zero

Solution

Since $\vec{A} \times \vec{B} = \vec{C}, \vec{C}$ must be perpendicular to the plane containing $\vec{A} and \vec{B}$ . Hence option (4) is correct. Also $\vec{C} . \vec{A} and \vec{C} . \vec{B}$ must be zero.

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