Let a and b be two vectors such that |a| = 1, |b| = 4 and a · b =… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 31 January, Shift 1Cross Product

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}| = 1$ , $|\vec{b}| = 4$ and $\vec{a} \cdot \vec{b} = 2$ . If $\vec{c} = (2\vec{a} \times \vec{b}) - 3\vec{b}$ and the angle between $\vec{b}$ and $\vec{c}$ is $\alpha$ , then $192 \sin^2(\alpha)$ is equal to:

A
$48$
B
$54$
C
$60$
D
$72$

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