Let a = 2i - j + 3k, b = 3i - 5j + k, and c be a vector such that… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 29 January, Shift 1Cross Product

Let $\mathbf{a} = 2\hat{i} - \hat{j} + 3\hat{k}$ , $\mathbf{b} = 3\hat{i} - 5\hat{j} + \hat{k}$ , and $\mathbf{c}$ be a vector such that $\mathbf{a} \times \mathbf{c} = \mathbf{c} \times \mathbf{b}$ and $(\mathbf{a} + \mathbf{c}) \cdot (\mathbf{b} + \mathbf{c}) = 168.$ Then the maximum value of $| \mathbf{c} |^2$ is:

A
$462$
B
$77$
C
$308$
D
$154$

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