Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them : 7x+5y+6z+30=0 and 3x-y-10z+4=0

Answer

The direction ratios of the normal to the given planes are 7, 5, 6 and 3, -1, -10 respectively.
`therefore costheta = (7xx3+5xx-1+6xx-10)/(sqrt(7^2+5^2+6^2) (sqrt(3^2+(-1)^2+(-10)^2) = (21-5-60)/(sqrt110) (sqrt110) = (-44)/110 = (-2)/5`
`therefore` The acute angle between the planes is give by ` costheta = 2/5 rArr theta = cos^(-) (2/5)`