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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