Find the angle between the planes whose vector equations are
`vec(r). (2 hati + 2 hatj - 3 hatk) = 5 and vec(r). (3 hati - 3 hatj + 5 hatk) = 3 `.

Find the angle between the planes whose vector equations are vecr.(2hati+2hatj-3hatk)=5 and vecr.(3hati-3hatj+5hatk)=3 .

Find the angle between the planes whose vector equations are barr *(2hati + 2hatj - 3hatk) = 5 and barr *(hati -2hatj+hatk) =7 .

Find the shortest distance between the lines whose vector equations are : vec(r) = (hati + 2 hatj + 3 hatk ) + lambda (hati -3 hatj + 2 hatk) and vec(r) = 4 hati + 5 hatj + 6 hatk + mu (2 hati + 3 hatj + hatk) .

Find the acute angle between the plane : vec(r). (hati - 2hatj - 2 hatk) = 1 and vec(r). (3 hati - 6 hatj + 2 hatk) = 0

Find the equation of a plane through the intersection of the planes : vec(r) ( 2 hati + hatj + 3 hatk) = 7 and vec(r). (2 hati + 3 hatj + 3 hatk) = 9 and passing through the point (2,1,3).

State Whether TRUE or FALSE: Angle between the planes : vec(r). (hati - 2 hatj - 2 hatk) = 1 and vec(r).(3 hati - 6 hatj + 2 hatk) = 0 is cos^(-1) ((11)/(21)) .

Find the shortest distance between the following (1-4) lines whose vector equations are : 1. vec(r) = hati + hatj + lambda (2 hati - hatj + hatk ) and vec(r) = 2 hati + hatj - hatk + mu (3 hati - 5 hatj + 2 hatk) .

Angle between the planes: (i) vec(r). (hati - 2 hatj - hatk) = 1 and vec(r). (3 hati - 6 hatj + 2 hatk) = 0 (ii) vec(r). (2 hati + 2 hatj - 3 hatk ) = 5 and vec(r) . ( 3 hati - 3 hatj + 5 hatk ) = 3

Find the equation of the plane , which contains the line of intersection of the planes : vec(r). (hati + 2 hatj + 3 hatk) -4 = 0 and vec(r). (2 hati + hatj + hatk) + 5 = 0 and which is perpendicular to the plane : vec(r) . (5 hati + 3 hatj - 6 hatk) ) + 8 = 0 .

Find the vector equation of the plane passing through the intersection of the planes vec(r). (2 hati + 2 hatj - 3 hatk) = 7, vecr(r). (2 hati + 5 hatj + 3 hatk ) = 9 and through the point (2,1,3).