Question

two position vectors lie in a plane. the first, vector \\(\vec{r}_a\\), points at an angle of 20.0° below the positive x - axis and has a magnitude of 57.0 m. the second, vector \\(\vec{r}_b\\), points at an angle of 43.0° above the positive x - axis and has a magnitude of 75 m.\
(a) choose the diagram below that is correct a graphical representation of \\(\vec{r}_a + \vec{r}_b\\)\
(b) what is the magnitude and direction of vector \\(\vec{r}_c\\)? give the direction as an angle measured counterclockwise from the positive x - axis?\
magnitude \\(\square\\) m\
direction \\(\square\\) ° (counterclockwise from the +x - axis)

Explanation:

Answer:

(a) The bottom-left diagram (showing $\vec{r}_A$ in the fourth quadrant, $\vec{r}_B$ in the first quadrant, and $\vec{r}_C = \vec{r}_A + \vec{r}_B$ using the tip-to-tail method).
(b) magnitude: $103\text{ m}$; direction: $11.0^\circ$