If a, b, c are three non-zero vectors and n is a unit vector perp… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 30 January, Shift 1Cross Product

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\mathbf{c}$ such that $\mathbf{a} = \alpha \mathbf{b} - \hat{n}, \quad (\alpha \neq 0)$ and $\mathbf{b} \cdot \mathbf{c} = 12, \quad then \quad \left| \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) \right|$ is equal to:

A
$15$
B
$9$
C
$12$
D
$6$

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