Question

The angle between the planes \(2x-y+z=6\) and \(x+y+2z=7\) is:

• A. \(0^\circ\)
• B. \(90^\circ\)
• C. \(60^\circ\)
• D. \(30^\circ\)

Hint:

Angle between planes equals angle between their normals.

Answer 1

The Correct Option is C

Normals: \(\vec{n_1}=(2,-1,1)\), \(\vec{n_2}=(1,1,2)\) \[ \cos\theta=\frac{\vec{n_1}\cdot\vec{n_2}}{|\vec{n_1}||\vec{n_2}|} =\frac{3}{\sqrt6\sqrt6}=\frac12 \Rightarrow \theta=60^\circ \]