JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q13

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MathematicsSingle correct+4 / -1Question 13 of 90

Let $\vec a=2\hat i-\hat j+5\hat k$ and $\vec b=\alpha\hat i+\beta\hat j+2\hat k$ . If $\left(\left(\vec a\times\vec b\right)\times\hat i\right)\cdot\hat k=\dfrac{23}2$ , then $\left|\vec b\times2\hat j\right|$ is equal to

\sqrt{21}

\sqrt{17}

Answer and worked solution

Official answer: B

Triple product. $(\vec v\times\hat i)\cdot\hat k=-v_2$ , and $v_2=5\alpha-4$ for $\vec v=\vec a\times\vec b$ . So $4-5\alpha=\frac{23}2$ , giving $\alpha=-\frac32$ .

Cross product. $\vec b\times2\hat j=2(-2,0,\alpha)$ , magnitude $2\sqrt{4+\frac94}=5$ .

(B)

Topics:Scalar and vector triple products Cross product

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 13