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Vector Triple Product

Let p, q and ...

Question

Let $\to p, \to q$ and $\to r$ be three non-coplanar unit vectors equally inclined to each other at an angle of $\frac{π}{3}$ . Then the value of $| \to p \times (\to q \times \to r) |$ is

A

3

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B

\frac{1}{2}

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C

\frac{\sqrt{3}}{4}

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D

\frac{3 \sqrt{3}}{4}

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Solution

The correct option is B $\frac{1}{2}$
$| \to p | = | \to q | = | \to r | = 1$

$| \to p \times (\to q \times \to r) |$
$= | (\to p . \to r) \to q - (\to p . \to q) \to r |$
$= ∣ ∣ ∣ | \to p | | \to r | cos (\frac{π}{3}) \to q - | \to p | | \to q | cos (\frac{π}{3}) \to r ∣ ∣ ∣$
$= cos (\frac{π}{3}) | \to q - \to r | = cos (\frac{π}{3}) \times \sqrt{(\to q - \to r) \cdot (\to q - \to r)} = \frac{1}{2} \times \sqrt{1 + 1 - 2 cos (\frac{π}{3})} = \frac{1}{2} \times \sqrt{1 + 1 - 1} = \frac{1}{2}$

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Vector Triple Product

Standard XII Mathematics

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