Let a = i + 2 j + k and b = 2 i + j - k. Let c be a unit vector i… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 8 April, Shift 2Basics of Vectors

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 perpendicular to $\vec{a}$ . Then such a vector $\hat{c}$ is:

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

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