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Linear Combination of Vectors

If r · a = ...

Question

If $r \cdot a = 0, r \cdot b = 0$ and $r \cdot c = 0$ for some nonzero vector $r$ , then the value of $[a b c]$ is

A

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B

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C

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D

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Solution

The correct option is C $0$
$r$ is vector perpendicular to $a, b, c$ .
Thus $r$ is the normal to the plane containing $a, b, c$ .
Or we can say that $a, b, c$ lie on the same plane whose normal is $r$ .
Hence $a, b, c$ are coplanar with respect to r.
Hence $[a b c] = 0$ .

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