In the following cases, determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.
(i) 2x – y + z = 6 and x + y + 2z = 7
(ii) `vecr.(hati-hatj+hatk)` and `vecr.(3hati+2hatj-hatk)-11=0`
(iii) x + y – 2z = 3 and 2x – 2y + z = 5
(iv) 2x – 3y + 4z = 1 and -x + y = 4
(v) `vecr.(2hati+3hatj-6hatk)=5` and `vecr.(hat i - 2 hatj+2hatk)=9`

Answer

(i) `pi/3`
(ii) `pi/2`
(iii) `cos^(-1)((2)/(3sqrt6))`
(iv) `cos^(-1)((5)/(sqrt(58)))`
(v) `cos^(-1)((16)/(21))`