JEE Main20258 Apr 2025Evening ShiftMathematicsVector AlgebraActual

Let a = i +2 j + k and b =2 i + j - k . Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a . Then such a vector c is :

Options

A1 5 ( j -2 k )
B1 3 (- i + j - k )
C1 3 ( i - j + k )
D1 2 (- i + k )

Correct answer

D. 1 2 (- i + k )

Step-by-step solution

Let vector p in plane of a & b =K( a + b ) aligned & p a = p a =0 & ~K ( a + b ) a =0 & a a + b a =0 & 6+ (3)=0 & =-2 & p =(-3 i +3 k ) aligned Unit vector (- i + k ) 2

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