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KCET2022MathematicsThree Dimensional Geometry

The angle between the pair of lines x+3 3 = y-1 5 = z+3 4 and x+1 1 = y-4 4 = z-5 2 is

Options

  1. A= ⁻¹ [ 27 5 ]
  2. B= ⁻¹ [ 8 3 15 ]
  3. C= ⁻¹ [ 19 21 ]
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Given, equation of lines are aligned x+3 3 & = y-1 5 = z+3 4 and x+1 1 & = y-4 4 = z-5 2 aligned Direction ratios of line (i) : Direction ratios of line (ii) : We know angle between pair of lines is given by = | a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 | where, and are direction ratios of respectively lines. aligned & = | 3 1+5 4+4 2 3^2+5^2+4^4 1^2+4^2+2^2 | & = | 3+20+8 9+25+16 1+16+4 |= | 31 5 2 21 |= 31 5 42 & = ⁻¹ ( 31 5 42 ) aligned

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