Question

For any θ, the vectors
U = cosθI+ sinθJ, V = −sinθI+ cosθJ,

form an orthonormal basis for the plane; that is, they are orthogonal vectors of length 1.
Let θ = [(2π)/6], and X = 8 I+ 6 J. Then we can write

X = uU+vV

with u = ? , v = ?