Let a = i + α j + β k, where α, β ∈ ℝ. Let b be a vector such tha… | JEE Main 2024 Mathematics PYQ

MCQEasyJEE Main 2024 · 30 January, Shift 2Cross Product

Let $\vec{a} = \hat{i} + \alpha \hat{j} + \beta \hat{k}$ , where $\alpha, \beta \in \mathbb{R}$ . Let $\vec{b}$ be a vector such that the angle between $\vec{a}$ and $\vec{b}$ is $\pi/4$ and $|\vec{b}| = 6$ . If $|\vec{a} \times \vec{b}| = 3\sqrt{2}$ , then the value of $(\alpha^2 + \beta^2)|\vec{a} \times \vec{b}|^2$ is equal to:

A
$90$
B
$75$
C
$95$
D
$85$

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