Find the angle between the planes `2x + y - 2z = 5 and 3x - 6y - 2z = 7`. Using vector method.

Answer

`cos^(-1)(4/21)`

Explanation

D.r.'s of normals to the given planes are 2,1,-2 and 3,-6,-2.
`therefore cos theta = |(2xx3)+1 xx (-6)+(-2)xx(-2)|/(sqrt(2^(2)+1^(2)+(-2)^(2))(sqrt(3^(2)+(-6)^(2)+(-2)^(2))`.
`4/(sqrt(9)sqrt(49))=4/(3 xx 7) = 4/21 rArr theta=cos^(-1)(4/21)`.