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MHT CET202313 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The acute angle between the line joining the points (2,1,-3),(-3,1,7) and a line parallel to x-1 3 = y 4 = z+3 5 through the point (-1,0,4) is

Options

  1. A⁻¹ ( 1 10 )
  2. B⁻¹ ( 5 7 10 )
  3. C⁻¹ ( 7 5 10 )
  4. D⁻¹ ( 3 5 10 )

Correct answer

C. ⁻¹ ( 7 5 10 )

Step-by-step solution

The d.r.s. of the line joining the points (2,1,-3) and (-3,1,7) are -5,0,10 The d.r.s. of the line parallel to line x-1 3 = y 4 = z+3 5 are 3,4,5 The angle between the lines having d.r.s. -5,0,10 and 3,4,5 is = | -5(3)+0(4)+10(5) 25+0+100 9+16+25 | aligned & = 35 25 10 & = ⁻¹ ( 7 5 10 ) aligned

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