TS EAMCET · Maths · Three Dimensional Geometry
A plane \(\pi\) passing through the point \(3 \bar{i}-4 \bar{j}+5 \bar{k}\) is parallel to the plane which passes through the point \(\bar{i}+\bar{j}-\bar{k}\) and perpendicular to the vector \(\bar{i}+2 \bar{j}-3 \bar{k}\). Then the cartesian equation of \(\pi\) is
- A \(3 x-4 y+5 z+20=0\)
- B \(2 x-y+3 z-25=0\)
- C \(x+2 y-3 z+20=0\)
- D \(4 x+5 y-6 z+38=0\)
Answer & Solution
Correct Answer
(C) \(x+2 y-3 z+20=0\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through \(\hat{i}+\hat{j}-\hat{k}\) and perpendicular to \(\hat{i}+2 \hat{j}-3 \hat{k}\) is \[ \begin{aligned} & 1(x-1)+2(y-1)-3(z+1)=0 \\ & x+2 y-3 z-6=0 \end{aligned} \] \(\because \quad \pi\) plane is parallel to \(x+2 y-3 z-6=0\) and passing through…
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