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MHT CET202310 May 2023Morning ShiftMathematicsVector AlgebraActual

The vector projection of AB on CD , where A (2,-3,0), B (1,-4,-2), C (4,6,8) and D (7,0,10) , is

Options

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

Correct answer

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

Step-by-step solution

aligned & AB =- i - j -2 k & CD =3 i -6 j +2 k aligned Vector projection of AB on CD aligned & =( AB CD ) CD | CD |^2 & =(-3+6-4) (3 i -6 j +2 k ) ( 3^2+(-6)^2+2^2 )^2 & = -1 49 (3 i -6 j +2 k ) aligned

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