JEE Main202524 Jan 2025Evening ShiftMathematicsVector AlgebraActual

Let a =3 i - j +2 k , ~b = a ( i -2 k ) and c = b k . Then the projection of c -2 j on a is :

Options

A2 14
B14
C3 7
D2 7

Correct answer

A. 2 14

Step-by-step solution

aligned & b = a ( i -3 k ) & = | array ccc i & j & k 3 & -1 & 2 1 & 0 & -2 array |=2 i +8 j + k & c = b k =8 i -2 j & c -2 j =8 i -4 j aligned Projection of ( i -2 j ) on a aligned & ( c -2 j ) a = 8,-4,0 3,-1,2 14 & = 28 14 =2 14 aligned

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