JEE Main20244 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let a unit vector which makes an angle of 60^ with 2 i +2 j - k and angle 45^ with i - k be C . Then C + (- 1 2 i + 1 3 2 j - 2 3 k ) is :

Options

A2 3 i - 1 2 k
B( 1 3 + 1 2 ) i + ( 1 3 - 1 3 2 ) j + ( 1 3 + 2 3 ) k
C2 3 i + 1 3 2 j - 1 2 k
D- 2 3 i + 2 3 j + ( 1 2 + 2 2 3 ) k

Correct answer

A. 2 3 i - 1 2 k

Step-by-step solution

C = C ₁ i + C ₂ j + C ₃ k C ₁ ^2+ C ₂ ^2+ C ₃ ^2=1 C (2 i +2 j - k )=| C | 9 60^ 2 C ₁+2 C ₂- C ₃= 3 2 C ₁- C ₃=1 C ₁+2 C ₂= 1 2 C ₁= 2 3 + 1 2 C ₂= -1 3 2 C ₃= 2 3 - 1 2

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