$|\vec{a}|=\sqrt{3},|\vec{b}|=5, \vec{b} \cdot \vec{c}=10$ and angle between $\bar{b}$ and $\bar{c}$ is…

$|\vec{a}|=\sqrt{3},|\vec{b}|=5, \vec{b} \cdot \vec{c}=10$ and angle between $\bar{b}$ and $\bar{c}$ is $\left(\frac{\pi}{3}\right)$. If $\vec{a}$ is perpendicular to $\vec{b} \times \vec{c}$, then value of $|\vec{a} \times(\vec{b} \times \vec{c})|$ is
  1. $15$
  2. $10 \sqrt{3}$
  3. $30$
  4. $10$

Solution

$|\vec{a} \times(\vec{b} \times \vec{c})|=|\vec{a}| \times|\vec{b} \times \vec{c}| \sin \frac{\pi}{2}$ from (i) and (ii) $|\vec{a} \times(\vec{b} \times \vec{c})|=\frac{15}{2} \times 4=30$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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