Question

if vector A×Balong z axis and directions of vectors A and B​

Answer 1

Answer:

Answer: negative x axis

Explanation:

As A and B are directed along y axis and z axis respectively, therefore they are mutually perpendicular to each other.

Cross product of two vectors gives the vector perpendicular to both the vectors, therefore if A and B are perpendicular to each other, then their resultant cross product will be perpendicular to the y-z plane, which is the x axis.

A x B = A B sin ∅ in x axis

but B x A = A B sin ∅ in - x axis

Answer 2

Since AxB is perpendicular to both A and B, they have to lie in the (x,y)-plane if C is to be along z. Also A and B can’t be along the same axis or AxB=0. If C is to be along the positive z axis, the vectors {A,B,C} must be a right hand system, and of course either A or B can’t be 0, but that’s the most you can say. So: any 2 nonzero, noncolinear vectors A and B in the (x,y) plane have AxB along the z-axis, and is along the positive z-axis if {A,B,k} is a right hand system, where k is the unit vector in the z-direction.