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AP EAMCET202021 Sep 2020Evening ShiftMathematicsVector AlgebraActual

Given, ( A B C ) such that (A ) is (2 i - j + k , B ) is ( i -3 j -5 k ) and (C ) is (3 i -4 j -4 k ), then ( A B C ) is

Options

  1. AAn equilateral triangle
  2. BA right-angled triangle
  3. CAn isosceles triangle
  4. DA scalene triangle

Correct answer

B. A right-angled triangle

Step-by-step solution

Vertices of ( A B C ) are given as (A ) is (2 i - j + k ) (B ) is ( i -3 j -5 k ) and (C ) is (3 i -4 j -4 k ) ( A B =- i -2 j -6 k , B C =2 i - j + k ) and ( C A = i -3 j -5 k ) ( gathered | A B |= 1+4+36 = 41 | B C |= 4+1+1 = 6 gathered ) and (| C A |= 1+9+25 = 35 ) ( | A B |^2=| B C |^2+| C A |^2 ) ( A B C ) is an right-angled triangle. Hence, option (b) is correct.

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