(Solved): Given: A pre-tensioned cable DE is attached between ground E and end D of the pipe structure shown ...

Given: A pre-tensioned cable $$\mathrm{DE}$$ is attached between ground $$\mathrm{E}$$ and end $$\mathrm{D}$$ of the pipe structure shown. The tension in cable $$\mathrm{DE}$$ is $$T_{\mathrm{DE}}$$. Let $${\vec{F}}_{DE}$$ represent the force vector on the structure at $$\mathrm{D}$$ due to the cable. Find: a) Write out $${\vec{F}}_{DE}$$ in terms of its Cartesian components. b) Determine the moment about point A due to $${\vec{F}}_{DE}$$ using $${\vec{r}}_{AD}\times {\vec{F}}_{DE}$$. c) Determine the moment about point A due to $${\vec{F}}_{DE}$$ using $${\vec{r}}_{AE}\times {\vec{F}}_{DE}$$. Compare your answer with what you found in part a) above. d) Determine the moment about point $$\mathrm{C}$$ due to $${\vec{F}}_{DE}$$. Write your answers as vectors and in terms of, at most: $$T_{\mathrm{DE}}$$ and $$d$$.