If \overrightarrow{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{a} is [2 Apr 2025 Shift 1]

Correct Answer is : 1√155(7∧i+9∧j+5∧k)

{1}/{\sqrt{155}}(7 \hat{i}+9 \hat{j}+5 \hat{k})

{1}/{\sqrt{155}}(7 \hat{i}+9 \hat{j}-5 \hat{k})

{1}/{\sqrt{155}}(-7 \hat{i}+9 \hat{j}-5 \hat{k})

{1}/{\sqrt{155}}(-7 \hat{i}+9 \hat{j}+5 \hat{k})

JEE Main 2 Apr 2025 Shift 1 Paper

Section: Mathematics

Question : 20 of 75

Marks: +1, -0

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is a nonzero vector such that its projections on the vectors 2

∧

−

∧

−2

∧

and

∧

are equal, then a unit vector along

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[2 Apr 2025 Shift 1]

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