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Vector Addition

A⃗ and B⃗ are...

Question

$\to A a n d \to B$ are two perpendicular vectors in a plane. $\to C$ is another vector perpendicular to the plane containing vectors $\to A a n d \to B$ . Which of the following of the relations is/ are possible?

A

\to A + \to B = \to C

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B

\to A + \to C = \to B

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C

\to A \times \to B = \to C

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D

\to A \times \to C = \to B

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Solution

The correct option is D $\to A \times \to C = \to B$
Since $\to C$ is perpendicular to both $\to A a n d \to B$ , the sum of any two cannot yield the third vector.
Hence choices (a) and (b) are not possible. Since $\to A$ is perpendicular to $\to B$ , the three vectors are mutually perpendicular. Hence choices (c) and (d) are possible.

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