QJEEM24Ma72cd: JEE Main 2024 Physics - Class 11 JEEM24Ma72cd Solution: Let a → = i ^ + α j ^ + β k ^ , α , β ∈ R . Let a vector b → be …

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QJEEM24Ma72cd: JEE Main 2024 Physics - Class 11 JEEM24Ma72cd Solution: Let a → = i ^ + α j ^ + β k ^ , α , β ∈ R . Let a vector b → be …

Let $\vec{a} = \hat{i} + α \hat{j} + β \hat{k}, α, β \in R$ . Let a vector $\vec{b}$ be such that the angle between $\vec{a}$ and $\vec{b}$ is $\frac{π}{4}$ and $| \vec{b} |^{2} = 6$ . If $\vec{a} \cdot \vec{b} = 3 \sqrt{2}$ , then the value of $(α^{2} + β^{2}) | \vec{a} \times \vec{b} |^{2}$ is equal to

Multiple Choice Options

A 85
B 90
C 75
D 95

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Accepted Answer

$\begin{aligned} | \vec{b} |^{2} = 6; | \vec{a} | | \vec{b} | \cos θ = 3 \sqrt{2} \\ | \vec{a} |^{2} | \vec{b} |^{2} \cos^{2} θ = 18 \\ | \vec{a} |^{2} = 6 \end{aligned}$

Also $1 + α^{2} + β^{2} = 6$

$α^{2} + β^{2} = 5$

to find

$\begin{aligned} (α^{2} + β^{2}) | \vec{a} |^{2} | \vec{b} |^{2} \sin^{2} θ \\ = (5) (6) (6) (\frac{1}{2}) \\ = 90 \end{aligned}$

QJEEM24Ma72cd: JEE Main 2024 Physics - Class 11 JEEM24Ma72cd Solution: Let a → = i ^ + α j ^ + β k ^ , α , β ∈ R . Let a vector b → be …

Multiple Choice Options

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