GATE 2017 EC (EC2) – Question 13
The smaller angle (in degrees) between the planes $x+y+z=1$ and $2x-y+2z=0$ is ________.
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Show answer and explanation
Correct answer: 54.0 to 55.0
Explanation
The angle between planes is the smaller angle between their normals $n_1=(1,1,1)$ and $n_2=(2,-1,2)$.
Their dot product is $3$, and their lengths are $\sqrt3$ and $3$. Thus $\cos\theta=|3|/(3\sqrt3)=1/\sqrt3$.
Therefore $\theta=\cos^{-1}(1/\sqrt3)=$ **54.7356°**, within the official interval 54–55°.