JEE Main202621 January 2026Morning ShiftMathematicsVector AlgebraActual

Let a =- i +2 j +2 k , ~b =8 i +7 j -3 k and c be vector such that a c = b . If c ( i + j + k )=4 , then | a + c |² is equal to :

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Correct answer

A. 27

Step-by-step solution

Let c = x i + y j + z k . From a c = b : z - y = 4 , z + 2x = 7 , y + 2x = 3 . From c ( i + j + k ) = 4 : x + y + z = 4 . Solving: y = -1 , z = 3 , x = 2 . c = 2 i - j + 3 k . a + c = (-1+2) i + (2-1) j + (2+3) k = i + j + 5 k . | a + c |^2 = 1 + 1 + 25 = 27 .

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