Chapter 12, Problem 6AAE

(a)

To determine

Calculate the length of vectors $T_1$ and $T_2$. Also show their magnitudes are $\left|T_1\right|=\frac{w\cos \beta }{\sin \left(\alpha +\beta \right)}$ and $\left|T_2\right|=\frac{w\cos \alpha }{\sin \left(\alpha +\beta \right)}$.

(b)

To determine

Find the value of $\alpha$ that minimizes the magnitude $\left|T_1\right|$, for a fixed $\beta$.

(c)

To determine

Find the value of $\beta$ that minimizes the magnitude $\left|T_2\right|$, for a fixed $\alpha$.