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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

The position vectors of the points P and Q with respect to the origin O are a   → = i ^ + 3   j ^ - 2   k ^ and b   → = 3   i ^ - j ^ - 2   k ^ , respectively. If M is a point on P Q → , such that O M → is the bisector of ∠ P O Q , then O M   → is :

Options

  1. A2   i   ^ - j   ^ + k   ^  
  2. B2   i   ^ + j   ^ - 2   k   ^
  3. C2   - i ^ + j ^ - k ^
  4. D2   i ^ + j ^ + k ^

Correct answer

B. 2   i   ^ + j   ^ - 2   k   ^

Step-by-step solution

Given that O P → = i ^ + 3   j ^ - 2   k ^ and O Q → = 3   i ^ - j ^ - 2   k ^ Since, O P   → = O Q → = 14 , ∆ P O Q is isosceles. Hence, the internal bisector O M → is perpendicular to P Q → and M is the midpoint of P Q → . Therefore, O M   → = 1 2   O P   → + O Q   → i ⏞ + 3 j ⏞ - 2 k ⏞ + 3 i ^ - j ^ - 2 k ^ 2 = 2   i ^ + j ^ - 2 k ^

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