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JEE MAIN 2021

26-02-2021 S1

Question

If $\vec{a} \quad$ and $\vec{b}$ are perpendicular, then $\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})))$ is equal to.

Select the correct option:

$\overrightarrow{0}$

$\frac{1}{2}|\vec{a}|^4 \vec{b}$

$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$

$|\overrightarrow{\mathrm{a}}|^4 \overrightarrow{\mathrm{~b}}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \vec{a} \cdot \vec{b}=0 \\ & \vec{a} \times(\vec{a} \times \vec{b})=(\vec{a} \cdot \vec{b}) \vec{a}-(\vec{a} \cdot \vec{a}) \vec{b}=-|\vec{a}|^2 \vec{b} \\ & \text { Now } \vec{a} \times\left(\vec{a} \times\left(-|\vec{a}|^2 \vec{b}\right)\right) \\ & =|\vec{a}|^2(\vec{a} \times(\vec{a} \times \vec{b})) \\ & =-|\vec{a}|^2\left(-|\vec{a}|^2 \vec{b}\right)=|\vec{a}|^4 \vec{b}\end{aligned}$

Question Tags

JEE Main

Mathematics

Easy

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