When do i use Right-hand rule to decide whether components of a x b are positive, negative, or 0?

Question

When is it 0? Can you give me an example?

Answer 1

If a and b are parallel then a x b will be 0.

If a is the vector <1,0,0> and b is the vector <1,0,0> then a x b will be 0.

Answer 2

If written as a X b, the direction of the resultant vector is given by the right-hand-screw rule, the vector is in the direction the screw would turn if a is rotated towards b. Or, let you fingers of your right hand point from a to b, the thumb is in the direction of the cross product. If written b X a, the direction is reversed (or negative), so b X a = -(a X b)