For what value of a are the vectors `vec(A) = a hati - 2hatj +hatk` and `vec(B) = 2a hati +a hat j - 4hatk` perpendicular to each other ?

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

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.

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

For what value of x , will the two vector A= 2hati + 2hatj -x hatk and B =2 hati - hatj - 3hatk are perpendicular to each other ?

For what value of x , will the two vector A= 2hati + 2hatj -x hatk and B =2 hati - hatj - 3hatk are perpendicular to each other ?

If the vectors vecP = a hati + a hatj + 3 hatk and vecQ = a hati - 2 hatj - hatk are perpendicular to each other . Find the value of a ?

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 vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .

What is the value of a, if two vectors vec P =hati+12 hatj+hatk and vec Q =2hati-ahatj+4hatk are perpendicular to each other ?