AP EAMCET · Maths · Three Dimensional Geometry
A line \(L\) passes through the points \((1,2,-3)\) and \((3,3-1)\) and a plane \(\pi\) passes through the points \((2,1,-2),(-2,-3,6)\), \((0,2,-1)\). If \(\theta\) is the angle between the line L and plane \(\pi\), then \(27 \cos ^2 \theta=\)
- A \(25\)
- B \(9\)
- C \(5\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Since equation of line \(L\) is \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z+3}{2}\) and equation of the plane is \(\left|\begin{array}{ccc}x-2 & y-1 & z+2 \\ -2-2 & -3-1 & 6+2 \\ 0-2 & 2-1 & -1+2\end{array}\right|=0\) \(\Rightarrow x+y+z=1\) Now, angle between line and plane is given…
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