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MHT CET202211 Aug 2022Morning ShiftMathematicsVector AlgebraActual

The vector projection of P Q on A B , where P (-2,1,3), Q (3,2,5), A (4,-3,5) and B (7,-5,-1) is

Options

  1. A1 49 (3 i -2 j -6 k )
  2. B1 7 (3 i -2 j +6 k )
  3. C(3 i -2 j -6 k )
  4. D1 7 (3 i -2 j -6 k )

Correct answer

A. 1 49 (3 i -2 j -6 k )

Step-by-step solution

aligned & P Q =(3+2) i +(2-1) j +(5-3) k =5 i + j +2 k & A B =(7-4) i +(-5+3) j +(-1-5) k =3 i -2 j -6 k aligned now vector projection of P Q on A B is ( P Q A B ) A B | A B |^2 = 5 3+1 (-1)+2 (-6) (3 i -2 j -6 k ) 3^2+(-2)^2+(-6)^2 = 1 49 (3 i -2 j -6 k )

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