If a is a non-zero vector such that its projections on the vector… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 2 April, Shift 1Dot Product

If $\vec{a}$ is a non-zero vector such that its projections on the vectors $2\hat{i} - \hat{j} + 2\hat{k},\ \hat{i} + 2\hat{j} - 2\hat{k}$ , and $\hat{k}$ are equal, then a unit vector along $\vec{a}$ is:

A
$\frac{1}{\sqrt{155}} (-7\hat{i} + 9\hat{j} + 5\hat{k})$
B
$\frac{1}{\sqrt{155}} (-7\hat{i} + 9\hat{j} - 5\hat{k})$
C
$\frac{1}{\sqrt{155}} (7\hat{i} + 9\hat{j} + 5\hat{k})$
D
$\frac{1}{\sqrt{155}} (7\hat{i} + 9\hat{j} - 5\hat{k})$

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