WBJEE · Maths · Three Dimensional Geometry
The equation of the plane through the point \((2,-1,-3)\) and parallel to the lines \(\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\) and \(\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\) is
- A \(8 x+14 y+13 z+37=0\)
- B \(8 x-14 y-13 z-37=0\)
- C \(8 x-14 y-13 z+37=0\)
- D None of the above
Answer & Solution
Correct Answer
(A) \(8 x+14 y+13 z+37=0\)
Step-by-step Solution
Detailed explanation
The equation of plane passing through \((2,-1,-3)\) is \(a(x-2)+b(y+1)+c(z+3)=0\) Also, as the plane is parallel is the given two lines, \(\therefore 3 a+2 b-4 c=0\) and \(2 a-3 b+2 c=0\) \(\Rightarrow \mathrm{a}=-8, \mathrm{~b}=-14, \mathrm{c}=-13\) \(\therefore\) The equation…
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