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

Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 hati + 9 hatj +3 hatk are parallel to each other.

Determine the area of the parallelogram whose adjacent sides are formed by the vectors vec(A) = hati - 3hatj + hatk and vec(B) = hati + hatj + hatk .

Find the unit vector parallel to the resultant of the unit vectors vec(A) = 2 hati - 6 hatj - 3hatk and vec(B) = 4 hati +3hatj - hatk .

Prove that the vectors vec(A) = hati +2 hatj +3hatk and vec(B) = 2hati - hatj are perpendicular to each other.

Find a vector whose length is 7 and which is perpendicular to each of the vectors, vec(A) = 2 hati - 3hatj + 6hatk and vec(B) = hati +hatj - hatk

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

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

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

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

Find unit vector parallel to the resultant of the vectors vec(A) = hati +4hatj +2hatk and vec(B) = 3hati - 5hatj +hatk .