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Applications of Cross Product

Let A,B,C b...

Question

Let $A, B, C$ be unit vectors. Suppose $A . B = A . C = 0$ and the angle between $B$ and $C$ is $\frac{π}{6} .$ Then $A$ equals

\pm 2 (B \times C)

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- 2 (B \times C)

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2 (B \times C)

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(B \times C)

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Solution

The correct option is D $\pm 2 (B \times C)$
Since $A . B = A . C = 0$
$∴ A$ is $⊥$ to the plane $B$ and $C$
Also, $B \times C = | B | | C | sin \frac{π}{6} ˆ n = \frac{1}{2} ˆ n$
But $A = ˆ n$ , both being unit vectors $⊥$ to the plane of $B$ and $C$
$A = \pm 2 (B \times C)$

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Let $A, B, C$ be unit vectors. Suppose $A . B = A . C = 0$ and the angle between $B$ and $C$ is $\frac{π}{6} .$ Then $A$ equals

The correct option is D $\pm 2 (B \times C)$
Since $A . B = A . C = 0$
$∴ A$ is $⊥$ to the plane $B$ and $C$
Also, $B \times C = | B | | C | sin \frac{π}{6} ˆ n = \frac{1}{2} ˆ n$
But $A = ˆ n$ , both being unit vectors $⊥$ to the plane of $B$ and $C$
$A = \pm 2 (B \times C)$