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Manipal MET2020MathematicsStraight Lines

If A(-1,3,2), B(2,3,5) and C(3,5,-2) are vertices of a A B C , then angles of A B C are

Options

  1. AA=90^ , B=30^ , C=60^
  2. BA= B= C=60^
  3. CA= B=45^ , C=90^
  4. DNone of the above

Correct answer

D. None of the above

Step-by-step solution

Given vertices of a A B C are aligned & A(-1,3,2), B(2,3,5) and C(3,5,-2) . & Now DR's of A B=(2+1,3-3,5-2)=(3,0,3) & DR's of B C=(3-2,5-3,-2-5)=(1,2-7) & and DR's of C A=(-1-3,3-5,2+2) &=(-4,-2,4) aligned Now, the angle between A B and B C , aligned B & = |3 1+0 2+3 (-7)| 3^2+0^2+3^2 1^2+2^2+(-7)^2 & = |3+0-21| 9+0+9 1+4+49 & = 18 3 2 3 6 = 2 2 3 = 1 3 aligned angle between B C and C A , aligned C & = |1 (-4)+2(-2)+(-7)(4)| 1^2+2^2+(-7)^2 (-4)^2+(-2)^2+(4)^2 & = |-4-4-28| 1+4+49 16+4+16 & = 36 54 36 = 36 3 6 6 & =

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