TS EAMCET · Maths · Three Dimensional Geometry
The foot of the perpendicular drawn from the point \((1,1,1)\) to the plane \(\pi_1\) is \((1,3,5)\). If \((2,2,-1),(3,4,2),(3,3,0)\) are three points on the plane \(\pi_2\), then the angle between the planes \(\pi_1\) and \(\pi_2\) is
- A \(\frac{\pi}{2}\)
- B \(\cos ^{-1}\left(\frac{1}{3}\right)\)
- C \(\frac{\pi}{6}\)
- D \(\cos ^{-1}\left(\frac{2}{5}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
We know that, foot of perpendicular from a point \(\left(x_1, y_1, z_1\right)\) on the plane \(a x+b y+c z+d=0\) is \((x, y, z)\) where \(\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}=\frac{-\left(a x_1+b y_1+c z_1+d\right)}{a^2+b^2+c^2}\) Since, the foot of the perpendicular…
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