Three Dimensional Geometry Question 365
Question: What is the angle between two planes $ 2x-y+z=4 $ and $ x+y+2z=6? $
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given equation of two planes are $ 2x-y+z=4 $ and $ x+y+2z=6 $ So, angle between them is $ \cos \theta =\frac{2(1)+(-1)(1)+(1)(2)}{\sqrt{4+1+1}\sqrt{4+1+1}} $ $ =\frac{2-1+2}{\sqrt{6}\sqrt{6}}=\frac{3}{6}=\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}. $
BETA
