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Vector Algebra question

2025 · 8 Apr · Shift 2 · Q43

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JEE Main
Mathematics
Vector Algebra
2025 · 8 Apr · Shift 2 · Q43

Vector Algebra question

2025 · 8 Apr · Shift 2 · Q43

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a} = \hat{i} + 2\hat{j} + \hat{k}

and

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

. Let

\hat{c}

be a unit vector in the plane of the vectors

\vec{a}

and

\vec{b}

and be perpendicular to

\vec{a}

. Then such a vector

\hat{c}

is:

A
$\frac{1}{\sqrt{2}}(-\hat{i} + \hat{k})$
B
$\frac{1}{\sqrt{5}}(\hat{j} - 2\hat{k})$
C
$\frac{1}{\sqrt{3}}(\hat{i} - \hat{j} + \hat{k})$
D
$\frac{1}{\sqrt{3}}(-\hat{i} + \hat{j} - \hat{k})$

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