The vector product of vectors A⃗ and B⃗ has magnitude 12.0 m2 and is in the +z-direction.Vector A⃗ has magnitude 4.0 m and is in
the −x-direction. Vector B⃗ has no x-component.Part A: What is the magnitude of vector B⃗ ? (I solved this question the answer is 3 and it's correct)Part B: What is the direction angle θ of vector B⃗ measured from the +y-direction to the +z-direction? (This is the part that I didn't get it correct)
The problem says that the vector product of A and B is in the +z-direction, and that the vector A is in the -x-direction. Since vector B has no x-component, and is perpendicular to the z-axis (as A and B are both perpendicular to their vector product), vector B has to be in the y-axis.
Using the right hand rule for vector product, we can test the two possible cases:
If vector B is in the +y-axis, the product AxB should be in the -z-axis. Since it is in the +z-axis, this is not correct.
If vector B is in the -y-axis, the product AxB should be in the +z-axis. This is the correct option.
Now, the problem says that the angle θ is measured from the +y-direction to the +z-direction. This means that the -y-direction has an angle of 180° (half turn).
