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 = ???

Answer 1

Using the equation \[x=Q^T*V\]
So, \[u=Q^T_1*V=4-3\sqrt{3}\]
\[u=Q^T_2*V=4\sqrt{3}+3\]

Answer 2

it says its not correct !

Answer 3

Let me check it.

Answer 4

thanks

Answer 5

Does
\[u=4+3*\sqrt3;v=-4*\sqrt3+3\]
correct?

Answer 6

yes thank you :D