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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

The point on the line x - 2 1 = y + 3 - 2 = z + 5 - 2 at a distance of 6 from the point 2 ,   - 3 , -   5 is

Options

  1. A3 , - 5 , - 3
  2. B4 , - 7 , - 9
  3. C0 , 2 , - 1
  4. D- 3 , 5 , 3

Correct answer

B. 4 , - 7 , - 9

Step-by-step solution

Let point is x - 2 1 = y + 3 - 2 = z + 5 - 2 = λ P ≡   λ + 2 ,   - 2 λ - 3 , - 2 λ - 5 Let, Q ≡ 2 ,   - 3 , - 5 Given, P Q = 6 ⇒ P Q 2 = 36 ⇒ λ + 2 - 2 2 + - 2 λ - 3 + 3 2 + 2 λ - 5 + 5 2 = 36 ⇒ 9 λ 2 = 36 ⇒ λ 2 = 4 ⇒ λ = ±   2 ∴ From λ = 2 ,   P ≡ 4 , - 7 , -   9 . And from λ = - 2 ,   P   ≡ 0 ,   1 ,   - 1 .

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