First slide

Vector triple product

Question

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

Moderate

A

0
B

⅔
C

3/5
D

¾

Solution

$\begin{array}{l} \vec{a} \times (\vec{a} \times \vec{b}) = \vec{c} \Rightarrow | \vec{a} | | \vec{a} \times \vec{b} | = | \vec{c} | \\ (∵ \vec{a} ⊥ (\vec{a} \times \vec{b})) \end{array}$
$1 (1 \times 5) \sin θ = 3 \Rightarrow \sin θ = \frac{3}{5} \Rightarrow \tan θ = \frac{3}{4}$

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