Hi i really need help on vectors. any reference sites that could help me on this type of questions would be good.
Q: Find a unit vector that is perpendicular to the vector u-4i-3j+5k and parallel to the xy plane.
I'm going to assume you mean "u= 4i- 3j+ 5k".
A vector is "parallel to the xy plane" if and only if it is of the form xi+ yj+ 0k for some numbers x, y.
For such a vector to be perpendicular to 4i+ 3j+ 5k we must have $\displaystyle (xi+ yj+ 0k)\cdot (4i- 3j+ 5k)= 4x- 3y= 0$ which is the same as 4x= 3y. Choose any number you like for either x or y and solve for the other. Finally, find the length of that vector and divide by the length to get a unit vector.