TS EAMCET · Maths · Three Dimensional Geometry
A plane \(\pi\) passes through the points \((5,1,2),(3,-4,6\) and \((7,0,-1)\). If \(p\) is the perpendicular distance from the origin to the plane \(\pi\) and \(l, m, n\) are the direction cosin of a normal to the plane \(\pi\), then \(|3 l+2 m+5 n|=\)
- A \(3 p\)
- B \(2 p\)
- C \(p\)
- D \(\frac{p}{2}\)
Answer & Solution
Correct Answer
(C) \(p\)
Step-by-step Solution
Detailed explanation
\(P(5,1,2), Q(3,-4,6), R(7,0,-1)\) Equation of \(P\) line passing through \(P Q R\) is \(\begin{aligned} & \left|\begin{array}{ccc} x-5 & y-1 & z-2 \\ 3-5 & -4-1 & 6-2 \\ 7-5 & 0-1 & -1-2 \end{array}\right|=0 \\ & \Rightarrow|9 x+2 y+12 z-12|=0 \end{aligned}\) Direction cosines…
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