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AP EAMCET202123 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If the line joining the points A(7, p, 2) and B(q,-2,5) is parallel to the line joining the points C(2,-3,5) and D(-6,-15,11) , then the value of p^2+q^2 is equal to

Options

  1. A25
  2. B16
  3. C9
  4. D7

Correct answer

A. 25

Step-by-step solution

aligned & (a) A(7, p, 2), B(q,-2,5) & C(2,-3,5), D(-6,-15,11) aligned Direction ratios of A B is given as, aligned & q-7,-2-p, 5-2 & a₁=q-7, b₁=-2-p, c₁=3 aligned Direction ratios of C D is given as, a₂=-8, b₂=-12, c₂=6 Given that, A B | C D a₁ a₂ = b₁ b₂ = c₁ c₂ aligned & & q-7 -8 & = -2-p -12 = 3 6 & & q-7 -8 & = 3 6 & & q-7 & =-4 & & q & =3 & and & -2-p -12 & = 3 6 aligned array lrl & p+2 & =6 p=4 & p^2+q^2 & =16+9=25 array

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