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 .

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

Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj +5hatk and vec(B) = hati - hatj +hatk .

The vector vec c , directed along the internal bisector of the angle between the vectors vec a = 7 hati - 4 hatj - 4hatk and vecb = -2hati - hatj + 2 hatk " with " |vec c| = 5 sqrt(6), is

Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3 hatk and vec(B) =- 2hati + hatj - 2hatk .

Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 hati + 9hatj +3hatk are parallel.

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

What is the angle between two vectors vec P =2hati +3hatj +hatk and vec Q =-3hati +6hatk .

Find the value of lambda so that the vectors vec(A) = 2hati + lambda hatj +hatk and vec(B) = 4hati - 2hatj - 2hatk are perpendicular to each other.