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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

Let A(3,2,-4) and B(9,8,-10) be two points. Let P₁ divide A B in the ratio 1: 2 and P₂ divide A B in the ratio 2: 1 . If the point P( , , ) divides P₁ P₂ in the ratio 1: 1 , then +2 +2 =

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

Let A(3,2,-4) and B(9,8,-10) be two points P , divide A B in 1: 2 So, coordinate of aligned & P₁ ( 2 3+9 3 , 2 2+1 8 3 , 2 (-4)+1(-10) 3 ) & P₁(5,4,-6) aligned Now, P₂ divide A B in 2: 1 . So, coordinate of P₂ ( 3+18 3 , 2+16 3 , -4-20 3 )=P₂(7,6,-8) If P divides P₁ P₂ in 1: 1 . So, coordinate of P ( 5+7 2 , 4+6 2 , -6-8 2 ) P(6,5,-7) But given that coordinate of P( , , ) . So, =6, =5 and =-7 Now, aligned +2 +2 & =6+2(5)+2(-7) & =6+10-14=2 aligned

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