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NDA2017MathematicsThree Dimensional GeometryActual

The points P (3,2,4), Q (4,5,2), R (5,8,0) and S (2,-1,6) are

Options

  1. Avertices of a rhombus which is not a square
  2. Bnon-coplanar
  3. Ccollinear
  4. Dcoplanar but not collinear

Correct answer

C. collinear

Step-by-step solution

aligned & P(3,2,4), Q(4,5,2), R(5,8,0), S(2,-1,6) & P Q= (4-3)^2+(5-2)^2+(2-4)^2 & = 1+9+4 = 14 & Q R= (5-4)^2+(8-5)^2+(0-2)^2 & = 1+9+4 = 14 & R S= (2-5)^2+(-1-8)^2+(6-0)^2 & = 9+81+36 = 126 =3 14 & P S= (2-3)^2+(-1-2)^2+(6-4)^2 & = 1+9+4 = 14 aligned Since, PQ + QR + PS = RS , points are collinear.

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