<s>[INST] Two unit vectors $x,y \in \mathbb{R}^n$ satisfying $x.y = \frac{\sqrt{3}}{2}$ Two unit vectors $x$ and $y$ in $\mathbb{R}^n$ satisfy x.y= $\frac{\sqrt{3}}{2}$
Evaluate 
A) angle between $x$ and $y$ in Radian. 
I got $\frac{\pi}{6}$
B) $y.(3x-5y)$
Looked at solving for $x$ and $y$, but think am going down completely the wrong way. In solving for $x$ and $y$ i isolated for $x$ to get $x =\frac{5y}2$
C)the length of $7x+2y$
 [/INST] Well, for the first question, we have - where $\phi$ is the angle between $x$ and $y$:
$$\cos\phi=\frac{x\cdot y}{|x||y|}=\frac{\sqrt{3}}{2}\Rightarrow\phi=\frac{\pi}{6}$$
since $\phi\in[0,\pi)$
For the second question, we have:
$$y\cdot(3x-5y)=y\cdot(3x)-5y\cdot y=3x\cdot y-5y^2=2\frac{\sqrt{3}}{2}-5|y|^2=3\frac{\sqrt{3}}{2}-5$$
For the third question, we have:
$$\begin{align*}|7x+2y|^2=&(7x+2y)^2=49x^2+28x\cdot y+4y^2=49|x|^2+28\frac{\sqrt{3}}{2}+4|y|^2=\\=&49+14\sqrt{3}+4=53+14\sqrt{3}\end{align*}$$
So 
$$|7x+2y|=\sqrt{53+14\sqrt{3}}$$
</s>