Find the angles between the following pairs of vectors:
(i) `vec(A) = hati + hatj +hatk` and `vec(B) =- 2hati - hatj - 2 hatk`.
(ii) `vec(A) =- 2hati +2hatj - hatk` and `vec(B) = 3hati + 6 hatj +2 hatk`
(iii) `vec(A) = 4 hati +6 hatj - 3 hatk` and `vec(B) =- 2hati - 5hatj +7 hatk`

Find the angles between the following pairs of vectors : vec A= hati + hatj + hatk and vec B = -2hati-2hatj-2hatk .

Find the angles between the following pairs of vectors : vec A= 2hati - 4hatj+ 6hatk and vec B=3hati +hatj +2hatk .

Find the angles between the following pairs of vectors : vec A= -2hati + 2hatj -hatk and vec B=3hati +6hatj +2hatk .

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 angle between the following pairs of lines : (i) vec(r) = 2 hati - 5 hatj + hatk + lambda (3 hati + 2 hatj + 6 hatk ) and vec(r) = 7 hati - 6 hatk + mu (hati + 2 hatj + 2 hatk) (ii) vec(r) = 3 hati + hatj - 2 hatk + lambda (hati - hatj - 2 hatk ) and vec(r) = 2 hati - hatj - 56 hatk + mu (3 hati - 5 hatj - 4 hatk) .

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2 hati - hatj - hatk and vec(c) = hati +3 hatj - 2hatk find (vec(a) xx vec(b)) xx vec(c)

Find the angle between the vectors vec A = hati + hatj + hatk and vec B =-hati - hatj + 2hatk .

Find the angle between the vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .

Find the angle between the vectors vec(A) = 2 hati - 4hatj +6 hatk and vec(B) = 3 hati + hatj +2hatk .

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2hati +hatj - hatk and vec(c) = hati +3hatj - 2hatk then find vec(a) xx (vec(b) xx vec(c)) .