Find the unit vector in the direction of $\langle-2,-1\rangle$. Write your answer in component form. Do not approximate any numbers in your answer.

Step 1 ：Given the vector \(\langle-2,-1\rangle\)

Step 2 ：Calculate the magnitude of the vector using the formula \(\sqrt{a^2 + b^2}\), where a and b are the components of the vector. In this case, a = -2 and b = -1. So, the magnitude is \(\sqrt{(-2)^2 + (-1)^2} = 2.23606797749979\)

Step 3 ：Find the unit vector by dividing each component of the vector by its magnitude. So, the unit vector is \(\langle\frac{-2}{2.23606797749979}, \frac{-1}{2.23606797749979}\rangle = \langle-0.8944271909999159, -0.4472135954999579\rangle\)

Step 4 ：Final Answer: The unit vector in the direction of \(\langle-2,-1\rangle\) is \(\boxed{\langle-0.8944271909999159, -0.4472135954999579\rangle}\)