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Question

Let $\to a, \to b$ and $\to c$ be the three vectors having magnitudes $1, 5$ and $3$ respectively, such that the angle between $\to a$ and $\to b$ is $θ$ and $\to a \times (\to a \times \to b) = \to c$ , then tan $θ$ is equal to

A

0

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B

\frac{2}{3}

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C

\frac{3}{5}

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D

\frac{3}{4}

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Solution

The correct option is D $\frac{3}{4}$
We have $\to a \times (\to a \times \to b) = \to c$
$\Rightarrow | \to a | | \to a \times \to b | = | \to c |$ as $(∵ \to a ⊥ (\to a \times \to b))$

$1 (1 \times 5) sin θ = 3$

$\Rightarrow sin θ = \frac{3}{5}$

$\Rightarrow tan θ = \frac{3}{4}$ ,

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