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AP EAMCET202124 Aug 2021Morning ShiftMathematicsVector AlgebraActual

If three consecutive vertices of a parallelogram are A(4,3,5), B(0,6,0) , C(-8,1,4) and D is the fourth vertex, then the angle between A C and B D is

Options

  1. A⁻¹ ( 65 149 161 )
  2. B⁻¹ ( 55 149 161 )
  3. C⁻¹ ( 73 149 161 )
  4. D⁻¹ ( 15 149 161 )

Correct answer

B. ⁻¹ ( 55 149 161 )

Step-by-step solution

Given, A(4,3,5), B(0,6,0), C(-8,1,4) and D are the vertices of a parallelogram Let D be the point (x, y, z) . Diagonals of parallelogram bisect each other. mid-point of A C= mid point of B D aligned & ( 4+(-8) 2 , 3+1 2 , 5+4 2 )= ( x+0 2 , y+6 2 , z+0 2 ) & (-2,2, 9 2 )= ( x 2 , y+6 2 , z 2 ) & x 2 =-2, y+6 2 =2, z 2 = 9 2 & x=-4, y=-2, z=9 aligned D is (-4,-2,9) . Now, A C = PV of C- PV of A aligned & =(-8 i + j +4 k )-(4 i +3 j +5 k ) & =-8 i + j +4 k -4 i -3 j -5 k & =-12 i -2 j - k B D & = PV of D- PV of B & =

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