Suppose \(\vec{C}=\vec{A}+\vec{B}\) where vector \(\vec{A}\) has components \(A_{x}=5\), \(A_{y}=2\) and vector \(\vec{B}\) has components \(B_{x}=-3, B_{y}=-5\).

a. What are the \(x\) - and \(y\)-components of vector \(\vec{C}\) ?

b. Draw a coordinate system and on it show vectors \(\vec{A}, \vec{B}\), and \(\vec{C}\).

c. What are the magnitude and direction of vector \(\vec{C}\) ?