Chapter 3, Problem 17P

GO ILW Three vectors $\stackrel{\to }{a}$, $\stackrel{\to }{b}$, and $\stackrel{\to }{c}$ each have a magnitude of 50 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 30°, 195°, and 315°, respectively. What are (a) the magnitude and (b) the angle of the vector $\stackrel{\to }{a}$ + $\stackrel{\to }{b}$ + $\stackrel{\to }{c}$, and (c) the magnitude and (d) the angle of $\stackrel{\to }{a}$ − $\stackrel{\to }{b}$ + $\stackrel{\to }{c}$? What are the (e) magnitude and (f) angle of a fourth vector $\stackrel{\to }{d}$ such that ( $\stackrel{\to }{a}$ + $\stackrel{\to }{b}$) − ( $\stackrel{\to }{c}$ + $\stackrel{\to }{d}$) = 0?