Let a = i + α j + β k, where α, β ∈ ℝ. Let b be a vector such that the angle between a and b is π/4 and |b| =…

Question

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 **$$|\vec{a} 	imes \vec{b}| = 3\sqrt{2}$$**, then the value of **$$(\alpha^2 + \beta^2)|\vec{a} 	imes \vec{b}|^2$$** is equal to:

Accepted Answer

A. $$90$$

Answer

B. $$75$$

Answer

C. $$95$$

Answer

D. $$85$$

Answer & step-by-step solution

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