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MHT CET202016 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The angle between the lines x-1 4 = y-3 1 = z 8 and x-2 2 = y+1 2 = z-4 1 is

Options

  1. A⁻¹ ( 3 4 )
  2. B⁻¹ ( 1 3 )
  3. C⁻¹ ( 1 2 )
  4. D⁻¹ ( 2 3 )

Correct answer

D. ⁻¹ ( 2 3 )

Step-by-step solution

(D) Let a and b be the vectors in the direction of the lines x-1 4 = y-3 1 = z 8 and x-2 2 = y+1 2 = z-4 1 respectively. a =4 i + j +8 k and b =2 i +2 j + k a b =(4 2)+(1 2)+(8 1)=8+2+8=18 Also | a | = 16+1+64 = 81 =9 and | b |= 4+1+4 = 9 =3 Let be the acute angle between the two given lines. = a b | a | | b | = 18 9 3 = 2 3 = ⁻¹ ( 2 3 )

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