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AP EAMCET202418 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let P ( , 4,7) and Q (3, , 8) are two points. If YZ - plane divides the join of the points P and Q in the ratio 2:3 and ZX - plane divides the join of P and Q in the ratio 4: 5 . then length of line segment PQ is

Options

  1. A107
  2. B27
  3. C83
  4. D97

Correct answer

A. 107

Step-by-step solution

Given, P( , 4,7) and Q(3, , 8) Since, YZ - plane divide the line joining the point P and Q in ratio =2: 3 So, its x -coordinate is zero 3 +2.3 2+3 =0 =-2 and ZX -plane divide the line joining the point P and Q in ratio 4: 5 So, its y-coordinate is zero 20+4 4+5 =0 =-5 Now, P (-2,4,7) and Q (3,-5,8) So, P Q= 5^2+(-9)^2+1^2 = 107

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