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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A line passes through the point A 2,3 , 5 and is parallel to the vector 2 i ^ - j ^ + k ^ . If P is a point on this line such that A P = 2 6 , then the coordinates of point P can be

Options

  1. A4,2 , 6
  2. B6,1 , 7
  3. C– 2,5 , – 3
  4. D2,3 , 5

Correct answer

B. 6,1 , 7

Step-by-step solution

Equation of the line through A 2,3 , 5 and parallel to 2 i ^ - j ^ + k ^ is x - 2 2 = y - 3 - 1 = z - 5 1 Coordinates of point P on this line are 2 λ + 2 , - λ + 3 , λ + 5 A P = 4 λ 2 + λ 2 + λ 2 = 2 6 ⇒ 6 λ 2 = 24 ⇒ λ = ± 2 Coordinates of point P can be 6,1 , 7 or – 2,5 , 3

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