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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

The position vector of the points A, B, C are (2 i + j - k ),(3 i -2 j + k ) and ( i +4 j -3 k ) respectively. These points

Options

  1. Aform an isosceles triangle
  2. Bform a right angled triangle
  3. Care collinear
  4. Dform a scalene triangle

Correct answer

C. are collinear

Step-by-step solution

A B =(3-2) i +(-2-1) j +(1+1) k aligned &= i -3 j +2 k | A B | &= 1+9+4 = 14 B C &=(1-3) i +(4+2) j +(-3-1) k &=-2 i +6 j -4 k aligned aligned | B C | &= 4+36+16 &= 56 =2 14 C A &=(2-1) i +(1-4) j +(-1+3) k &= i -3 j +2 k | C A | &= 1+9+4 = 14 aligned So, | A B |+| A C |=| B C | and angle between A B and B C is 180^ . Points A, B, C cannot form an isosceles triangle. Hence, A, B, C are collinear.

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