cross product with scalars: Given A=4a_x-2a_y+6a_z, find a_x x(cross) A

[Tramachine]

In my electromagnetics class, I am given a vector A=4a_x-2a_y+6a_z and asked to find a_x x(cross) A. it appears to be a cross product but does it just work as a scalar multiplier? so the answer would be (4*4,4*-2,4*6)? or is it handled a different way? The textbook doesn't touch on this and the rest of the internet has also been unfruitful.

 

[barrick]

In my electromagnetics class, I am given a vector A=4a_x-2a_y+6a_z and asked to find a_x x(cross) A. it appears to be a cross product but does it just work as a scalar multiplier? so the answer would be (4*4,4*-2,4*6)? or is it handled a different way? The textbook doesn't touch on this and the rest of the internet has also been unfruitful.

Hi Tramachine,

I think that the notation means that \(\displaystyle a_x\), \(\displaystyle a_y\) and \(\displaystyle a_z\) are the unit vectors on the coordinate axes, and (4,-2,6) are the coordinates of A with respect to that basis.

\(\displaystyle a_x=(1,0,0)\) is just an ordinary vector, and you must compute \(\displaystyle (1,0,0)\times(4,-2,6)\).