Question

Find the acute angle between the planes `barr*(2hati + hatj - hatk) = 3` and `barr*(hati + 2hatj + hatk) =1`.

Answer 1

Angle between two planes is given by
` cos theta = (|A_(1)*A_(2)+B_(1)*B_(2)+C_(1)*C_(2)|)/(sqrt(A_(1)^(2)+B_(1)^(2)+C_(1)^(2.))sqrt(A_(2)^(2)+B_(2)^(2)+C_(2)^(2)))`
` A_(1) = 2, B_(1) = 1, C_(1) = - 1`
` A_(2) = 1, B_(2) = 2, C_(2) = 1`
`cos theta = (|(2 xx 1)+(1xx2)+(-1 xx1)|)/(sqrt((2)^(2)+(1)^(2)+(-1)^(2))sqrt((1)^(2)+(2)^(2)+(1)^(2)))`
` cos theta = 3/6 = 1/2 `
` :. theta = pi/3`
` :. ` Angle between the planes is ` pi/3`.