Three vectors $\overrightarrow{A},\overrightarrow{ B}$ and $\overrightarrow{C}$ are such that $\overrightarrow{A}=\overrightarrow{B}+\overrightarrow{C}$ and their magnitudes are in ratio $5: 4: 3$ respectively:
Find angle between vector $\overrightarrow{A}$ and $\overrightarrow{C}$

Six vectors, $\overrightarrow{a}$ through $\overrightarrow{f}$ have the mangitudes and directions indicated in the figure. Which of the following statements is true?

In the cube of side $\text{'}a\text{'}$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be : 

Suppose $u$ and $v$ are differentiable functions of $x$ and $u\left(1\right)=2, u^{\text{'}}\left(1\right)=0, v\left(1\right)=5, v^{\text{'}}\left(1\right)=-1.$ Find the values of the following derivatives at $x=1.$

(a)$\frac{d}{dx}\left(uv\right)$ 
(b) $\frac{d}{dx}\left(\frac{u}{v}\right)$
(c) $\frac{d}{dx}\left(\frac{v}{u}\right)$
(d) $\frac{d}{dx}\left(7v-2u\right)$