Walker, Halliday & Resnick — Vectors: Problem 15

15 The two vectors \(\vec{a}\) and \(\vec{b}\) in Fig. 3-23 have equal magnitudes of 10.0 m and the angles are \(\theta_1 = 30^\circ\) and \(\theta_2 = 105^\circ\). Find the (a) x and (b) y components of their vector sum \(\vec{r}\), (c) the magnitude of \(\vec{r}\), and (d) the angle \(\vec{r}\) makes with the positive direction of the x axis.