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JEE Main2016MathematicsVector AlgebraActual

In a triangle A B C , right angle at vertex A , if the position vectors of A , B and C are respectively 3 i ^ + j ^ - k ^ , - i ^ + 3 j ^ + p k ^ and 5 i ^ + q j ^ - 4 k ^ , then the point p , q lies on a line:

Options

  1. AMaking an obtuse angle with the positive direction of x - a x i s
  2. BParallel to x - a x i s
  3. CParallel to y - a x i s
  4. DMaking an acute angle with the positive direction of x - a x i s

Correct answer

D. Making an acute angle with the positive direction of x - a x i s

Step-by-step solution

A B → =   - 4 i ^ + 2 j ^ + p + 1 k ^ A C → =   2 i ^ + q - 1 j ^ - 3 k ^ A B → ⊥ A C → ⇒ A B →   ·   A C → = 0 - 8 + 2 q - 1 - 3 p + 1 = 0 3 p - 2 q + 13 = 0 p , q lies on 3 x - 2 y + 13 = 0 Slope = 3 2 ∴   The required line makes an acute angle with the positive direction of x - axis.

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