ANSWER
[tex]< \frac{1}{5} , - \frac{1}{3} \: >[/tex]
EXPLANATION
The given vector , u has the following components,
[tex]u = < \: - 5 , - 3 \: > [/tex]
If two vectors are orthogonal, then their dot product is zero.
[tex]< \: - 5 , - 3 \: > \bullet < \: \frac{1}{5} , - \frac{1}{3} \: > = - 5 \times \frac{1}{5} \times - 3 \times - \frac{1}{3} = - 1 + 1 = 0[/tex]
Hence,the vector
[tex] < \frac{1}{5} , - \frac{1}{3} \: >[/tex]
is orthogonal to vector u.
