Question

A vector A points vertically upwards and vector B points towards north. What is the direction and magnitude of vector product A*B?

A vector A points vertically upwards and vector B points towards north. What is the direction and magnitude of vector product **A *B ?

Answer 1

Assuming that you meant to ask for the cross product, `vec Axx vecB`, the product is a vector with magnitude `A*B` and the direction is West.

Explanation:

Your notation does not make the question clear. There are 2 types of vector products.

Dot product:
The notation is `vec A * vecB` and the result is a scalar with magnitude `A*B*cosphi` where `phi` is the angle between `vec A and vecB`.

If you need the dot product of your 2 vectors, the result is zero because the angle between your vectors is `90^@ and cos90^@ = 0`.

Cross product:
The notation is `vec Axx vecB` and the result is a vector with magnitude `A*B*sinphi` where `phi` is the angle between `vec A and vecB`.

If you need the cross product of your 2 vectors, the result is a vector with magnitude `A*B -("note that " sin90^@ = 1`).

Determining the direction of this vector requires application of the right-hand-rule. I will give instructions below specifically for this problem, but open this website for a visual aid.
http://hyperphysics.phy-astr.gsu.edu/hbase/vvec.html#vvc5

Open your right hand with palm away from you and point the fingers up, `-` the direction of vector `vec A`. Face north and curl your fingers to horizontal, `-` the direction of vector `vec B`. Extend your thumb `-` that will be West. So the cross product points West.

I hope this helps,
Steve