Find the angle between the planes.
`vecr.(hati+hatj+2hatk)=5` and `vecr.(2hati-hatj+hatk)=8`.

Explanation

We know that the angle between the planes `vecr.vecn_(1)=q_(1)` and `vecr.vecn_(2)=q_(2)` is given by
`costheta=|(vecn_(1).vecn_(2)|/(vecn_(1)|vecn_(2)|`
Here, `vecn_(1)=(hati+hatj+2hatk)` and `vecn_(2)=(2hati-hatj+hatk)`.
`therefore costheta=|(hati+hatj+2hatk).(2hati-hatj+hatk)|/(|hati+hatj+2hatk||2hati-hatj+hatk|)`
`=|1 xx 2+1 xx (-1) + 2 xx 1|/(sqrt(1^(2)+1^(2)+2^(2))sqrt(2^(2)+(-1)^(2)+1^(2)))=3/6=1/2`.
`rArr theta=pi/3`.
Hence, the angle between the given planes is `(pi/3)`.