MHT CET20226 Aug 2022Morning ShiftMathematicsVector AlgebraActual

Let a = i + j + k , b = i - j + k and c = i - j - k be three vectors. A vector V in the plane of a and b , whose projection on c is 1 3 is given by

Options

Ai +3 j -3 k
B3 i - j +3 k
Ci -3 j +3 k
D-3 i -3 j - k

Correct answer

B. 3 i - j +3 k

Step-by-step solution

Any vector in the plane of a and b can be written as v = a + b =( i + j + k )+ ( i - j + k ) A Q Its projection on c is 1 3 aligned & ( a + b ) c | c | = 1 3 & (1+ )-(1- )-(1+ ) 1^2+(-1)^2+(-1)^2 = 1 3 & =2 aligned Putting =2 in eq. (1) we get v =3 i -2 j +3 k

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