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Vector Algebra question

2025 · 2 Apr · Shift 1 · Q38

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JEE Main
Mathematics
Vector Algebra
2025 · 2 Apr · Shift 1 · Q38

Vector Algebra question

2025 · 2 Apr · Shift 1 · Q38

JEE MainMathematicsVector AlgebraMCQ+4 / −1

If

\overrightarrow{\mathrm{a}}

is a nonzero 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

\overrightarrow{\mathrm{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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