If a is a nonzero vector such that its projections on the vectors 2i-j+2k, i+2j-2k, and k are equal, then a unit vector along a is:

(A) 1/(√(155))(-7i + 9j + 5k)

(B) 1/(√(155))(-7i + 9j - 5k)

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q36

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

\vec{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

\vec{a}

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q36

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

\vec{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

\vec{a}

is: