Maths · Equation of a line; Skew lines, the shortest distance between them and its equation

The equation of the plane passing through the intersection of the planes and and

The equation of the plane passing through the intersection of the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6} \) and \( \boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}= \) \( 0, \) and the point (1,1,1) is

  • A. \( 20 x+23 y+26 z-69=0 \)
  • B. \( 20 x+23 y+26 z+69=0 \)
  • C. \( 23 x+20 y+26 z-69=0 \)
  • D. None of these

Step-by-step solution

The equation of a plane through the intersection of the given planes is (x+y+z-6) + k(2x+3y+4z+5)=0. Substituting the point (1,1,1) gives -3+14k=0, so k=3/14. Multiplying by 14 yields 20x+23y+26z-69=0.
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