Let a, b, c be three non-zero vectors such that b · c = 0 and a ×… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 25 January, Shift 1Cross Product

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that $\vec{b} \cdot \vec{c} = 0$ and $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} - \vec{c}}{2}$ . If $\vec{d}$ is a vector such that $\vec{b} \cdot \vec{d} = \vec{a} \cdot \vec{b}$ , then $(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d})$ is equal to:

A
$1$
B
$\frac{1}{4}$
C
$2$
D
$\frac{1}{2}$

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