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Angle between Two Lines

A⃗ and B⃗ a...

Question

$\to A$ and $\to B$ are two vectors in a plane at an angle of $60^{0}$ with each other. $\to C$ is another vector perpendicular to the plane containing vectors $\to A$ and $\to B$ . Which of the following relations is possible?

\to A + \to B = \to C

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\to A + \to C = \to B

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

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

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Solution

The correct option is A $\to A \times \to B = \to C$
Vector C is perpendicular to both vectors A and B. Hence, it can be equal to their cross product.
Options A and B make vector C in the plane of vectors A and B which is not possible.
In option D, this is not possible as vector B is not perpendicular to vector A

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