JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 90

Let $\vec a=3\hat i+\hat j$ and $\vec b=\hat i+2\hat j+\hat k$ . Let $\vec c$ be a vector satisfying $\vec a\times(\vec b\times\vec c)=\vec b+\lambda\vec c$ . If $\vec b$ and $\vec c$ are non-parallel, then the value of λ is :

−5

−1

Answer and worked solution

Official answer: A

Expand. $(\vec a\cdot\vec c)\vec b-(\vec a\cdot\vec b)\vec c=\vec b+\lambda\vec c$ . Since $\vec b,\vec c$ are independent, $\lambda=-\vec a\cdot\vec b=-5$ .

(A)

Topics:Scalar and vector triple products

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 10