JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q16

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MathematicsSingle correct+4 / -1Question 16 of 90

If $\vec a\cdot\vec b=1$ , $\vec b\cdot\vec c=2$ and $\vec c\cdot\vec a=3$ , then the value of $\left[\vec a\times\left(\vec b\times\vec c\right),\ \vec b\times\left(\vec c\times\vec a\right),\ \vec c\times\left(\vec b\times\vec a\right)\right]$ is :

-6\vec a\cdot\left(\vec b\times\vec c\right)

12\vec c\cdot\left(\vec a\times\vec b\right)

-12\vec b\cdot\left(\vec c\times\vec a\right)

Answer and worked solution

Official answer: A

Expand. $\vec a\times(\vec b\times\vec c)=3\vec b-\vec c$ , $\vec b\times(\vec c\times\vec a)=\vec c-2\vec a$ , $\vec c\times(\vec b\times\vec a)=3\vec b-2\vec a$ .

Dependent. The third vector is the sum of the first two, so the box product is 0.

(A)

Topics:Scalar and vector triple products

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JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 16