JEE Main20252 Apr 2025Morning ShiftMathematicsVector AlgebraActual

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

Options

A1 155 (-7 i +9 j +5 k )
B1 155 (-7 i +9 j -5 k )
C1 155 (7 i +9 j +5 k )
D1 155 (7 i +9 j -5 k )

Correct answer

C. 1 155 (7 i +9 j +5 k )

Step-by-step solution

Let a = a ₁ i + a ₂ j + a ₃ k a ₁^2+ a ₂^2+ a ₃^2=1 Let b =2 i - j +2 k , c = i -2 j -2 k d = k a b | b | = a c | c | = a d | d | 2 a ₁- a ₂+2 a ₃ 3 = a ₁+2 a ₂-2 a ₃ 3 = a ₃ By solving a ₁= 7 155 , a ₂= 9 155 , a ₃= 5 155

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