AP EAMCET · Maths · Three Dimensional Geometry
If \(\mathrm{P}(2, \beta, \alpha)\) lies on the plane \(x+2 y-z-2=0\) an \(\mathrm{Q}(\alpha,-1, \beta)\) lies on the plane \(2 x-y+3 z+6=0\) then 1 direction cosines of the line PQ are
- A \(\left(-\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)\)
- B \(\left(+\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)\)
- C \(\left(\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)\)
- D \(\left(-\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(-\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } P(2, \beta, \alpha) \text { lies on } x+2 y-z-2=0 \\ & \Rightarrow 2+2 \beta-\alpha-2=0 \\ & \Rightarrow \alpha=2 \beta ...(i)\\ & Q(\alpha,-1, \beta) \text { lies on } 2 x-y+3 z+6=0 \\ & \Rightarrow 2 \alpha+3 \beta+7=0 \end{aligned}\)...(ii)…
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