u x v= (u_{y}v_{z}-u_{z}v_{y})i + (u_{z}v_{x}-u_{z}v_{z})j + (u_{x}v_{y}-u_{y}v_{x})k where u_{x} is the x component of U

u=u_{x}i+u_{y}j+u_{z}k and likewise for v

1. you were given the components of u and v using the above definition of the cross product calculate the vector a=uxb. The next step is to recall that if two vectors are orthogonal then one is perpendicular to the other and the dot product is zero. So you have to show that a• u =0 and a•v =0

u cross v is the definition of the vector cross product you calculate the components by multiplying the components of u and v together as I've shown above.

Would you like me to work the whole problem for you completely?

you were given u an v as components u=<-3,2,3>
v=<0,1,0>

so u=-3i+2j+3k and v=j

and u x v= (uyvz-uzvy)i + (uzvx-uxvz)j + (uxvy-uyvx)k =(2*0-3*1)i+(3*0-(-3)*(0))j + (-3*1-2*0)K=-3i+0j-3K=u cross v and this vector is perpendicular to v because (-3i-3k)•j=0 because i and k are perpendicular to j so i•j=0 and k•j=0.

## Comments

v=<0,1,0>