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

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let

\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}

\alpha, \beta \in \mathbb{R}

. Let a vector

\vec{b}

be such that the angle between

\vec{a}

and

\vec{b}

\frac{\pi}{4}

and

|\vec{b}|^2 = 6

. If

\vec{a} \cdot \vec{b} = 3\sqrt{2}

, then the value of

(\alpha^2 + \beta^2)|\vec{a} \times \vec{b}|^2

is equal to

Official answer

Option 2

NTA final key.