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Manipal MET2019MathematicsThree Dimensional Geometry

If (3,4,5), Q(4,6,3), R(-1,2,4), S(1,0,5) , then the projection of R S on P Q is

Options

  1. A- 2 3
  2. B- 4 3
  3. C1 2
  4. D2

Correct answer

B. - 4 3

Step-by-step solution

We have, P(3,4,5), Q(4,6,3), R(-1,2,4) and S(1,0,5) . Direction ratios of P Q are (1,2,-2) and direction cosines of P Q are 1 1^2+2^2+(-2)^2 , 2 1^2+2^2+(-2)^2 -2 1^2+2^2+(-2)^2 = 1 9 , 2 9 ,- 2 9 = 1 3 , 2 3 ,- 2 3 Required projection of R S on P Q is l (x₂-x₁ )+m (y₂-y₁ )+n (z₂-z₁ )

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