Find the angle between the plane:`7x+5y+6z+30=0 and 3x-y-10z+4=0`

Explanation

We know that the acute angle between the planes `a_(1)x+b_(1)y+c_(1)z+d_(1)=0` and `a_(2)x+b_(2)y+c_(2)z+d_(2)=0` is given by
`costheta=|a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)|/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2)sqrt(3^(2)+(-1)^(2)+(-10)^(2))`
`=|21-5-60|/(sqrt(49+25+36)sqrt(9+1+100))`
`=44/(sqrt(110) xx sqrt(110))=44/110=2/5`.
`rArr theta=cos^(-1)(2/5)`.
Hence, the acute angle between the given planes is `cos^(=1)(2/5)`.