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Vector Algebra question

2025 · 29 Jan · Shift 2 · Q30

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JEE Main
Mathematics
Vector Algebra
2025 · 29 Jan · Shift 2 · Q30

Vector Algebra question

2025 · 29 Jan · Shift 2 · Q30

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\hat{a}

be a unit vector perpendicular to the vectors

\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}

and

\vec{c} = 2\hat{i} + 3\hat{j} - \hat{k}

, and

\hat{a}

makes an angle of

\cos^{-1} \left( -\frac{1}{3} \right)

with the vector

\hat{i} + \hat{j} + \hat{k}

. If

\hat{a}

makes an angle of

\frac{\pi}{3}

with the vector

\hat{i} + \alpha\hat{j} + \hat{k}

, then the value of

a

is:

A
$\sqrt{3}$
B
$\sqrt{6}$
C
$-\sqrt{6}$
D
$-\sqrt{3}$

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