Question

The vector a1i + a2j + a3k and b1i + b2j + b3k are perpendicular to each other if

Answer 1

Answer:

... if their dot product (aka scalar product) is equal to zero.

In symbols

... if a₁ b₁ + a₂ b₂ + a₃ b₃ = 0

Answer 2

Question :

The vector a1i + a2j + a3k and b1i + b2j + b3k are perpendicular to each other if .

Given :

A = A₁i + A₂j

B = B₁i + Bj

To find :

The direction of the cross product of A and B.

Solution :

The cross product also known as the vector product of A and B:

A×B = |A||B| sinθ n

Here θ is the angle between the two vectors A and B and is between 0, π including the upper and lower limits.

And n is the unit vector which is perpendicular to both the vectors and can be founded out by the right handed system.

Here A and B vectors are in x-y plane therefore n must be in z axis.

Therefore the direction of cross product of A and B is k (along z-axis).

Thank you.