In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.
(a) `7x+5y+6z+30=0 and 3x-y-10 z+4=0`
(b) `2x+y+3z-2=0 and x-2y+5z=0`
(c)`2x-2y+4z+5=0 and 3x-3y+6z-1=0`
(d)`2x-y+3z-1=0and 2x-y+3z+3=0`
(e)`4x+8y+z-3=0and y+z-4=0`

Explanation

(a) `7x+5y+6z+30=0 and 3x-y-10z+4=0`

The direction Ratios are 7,5,6 and 3,-1-10.

Thus, angle between them is

`cosA=|(ab+cd+ef)/(sqrt(a^2+c^2+e^2)sqrt(b^2+d^2+f^2))|`

`cosA=|(21-5-60)/(sqrt(7^2+5^2+6^2)sqrt(3^2+1^2+10^2))|`

`cosA=44/110`

`A=cos^-1(2/5)`


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