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MHT CET202415 May 2024Evening ShiftMathematicsVector AlgebraActual

If the points P, Q and R are with the position vectors i -2 j +3 k ,-2 i +3 j +2 k and -8 i +13 j respectively, then these points are

Options

  1. Acollinear and Q lies between P and R .
  2. Bcollinear and R lies between P and Q .
  3. Ccollinear and P lies between Q and R .
  4. Dnon-collinear.

Correct answer

A. collinear and Q lies between P and R .

Step-by-step solution

aligned P Q & =-2 i +3 j +2 k -( i -2 j +3 k ) & =-3 i +5 j - k Q R & =-8 i +13 j -(-2 i +3 j +2 k ) & =-6 i +10 j -2 k & =2(-3 i +5 j - k )=2 P Q aligned QR is a scalar multiple of PQ . QR and PQ are parallel to each other with point Q in common. Points P , Q and R are collinear and Q lies between P and R .

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