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AP EAMCET202317 May 2023Morning ShiftMathematicsVector AlgebraActual

If 2 i + j - k , i -3 j +5 k and -3 i +4 j +4 k are the position vectors of three points A, B and C respectively, then

Options

  1. AABC is a right angled triangle
  2. BABC is an isosceles triangle
  3. CA , B , C are collinear points
  4. DABC is a scalene triangle

Correct answer

D. ABC is a scalene triangle

Step-by-step solution

aligned (d) O A =2 i + j - k , O B = i -3 j +5 k , O C=-3 i +4 j +4 k A B = O B - O A =- i +4 j +6 k | A B |= 1+16+36 = 53 B C = O C - O B =-4 i +7 j - k | B C |= 16+49+1 = 66 C A = O A - O C =5 i -3 j -5 k | C A |= 25+9+25 = 59 | A B | | B C | | C A | aligned A B C is a scalene triangle.

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