Any vector in the xy-plane has the form v = c1i + c2j + 0k
For v to be perpendicular to a, we need v · a = 0
So, 3c1 - 5c2 = 0
For example, choose c1 = 5 and c2 = 3.
Then v = 5i + 3j + 0k is perpendicular to a.
ll v ll = √[52 + 32 + 02] = √34
A unit vector in the xy-plane that is perpendicular to 3i - 5j + k is:
u = v / llvll = (5/√34)i + (3/√34)j + 0k
