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 ?

Vectors vecP=hati+2hatj+3hatk and vecQ=2hati+ahatj-5hatk are perpendicular .Find a.

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.

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 ?

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

For what value of a ,will the vectors ahati-2hatj+hatk and 2ahati+ahatj-4hatk be perpendicular to each other ?

Show that the vector vecA = -6hati + 9hatj - 12 hatk and vec = 2 hati - 3hatj + 4hatk are parallel 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.