Relative motion involving angle Suppose I am going in a direction with a velocity $v_1$ and my friend is going in a direction which makes an angle of $A$ with my direction with a velocity of $v_2$. 
Then what will  be my relative motion with respect to my friend or his relative motion with respect to me?
Every book I have read gave example where two things are going parallel or opposite of me. But I've never found any example with an angle.
 A: Let's say your velocity is $\vec{v}_1$ is 
$$\vec{v}_1= v_{1x}\hat{i} + v_{1y}\hat{j}$$
and your friends velocity $\vec{v}_2$ is 
$$\vec{v}_2= v_{2x}\hat{i}+v_{2y}\hat{j}$$
Then your velocity relative to your friend will be 
$$\vec{v}_r = (v_{1x}-v_{2x})\hat{i} + (v_{1y}-v_{2y})\hat{j}$$
The components can be found by considering an appropriate coordinate system. In this case that will be a coordinate system with the $x$-axis aligned with your friends velocity. In that case $v_{2y} =0$. While the components of your velocity will be $v_{1x}=v_{1}\cos{A}$ and $v_{1y}=v_{1}\sin{A}$.
Hope this helps.
A: You could always break the question into two perpendicular directions
Your velocity will be subtracted from horizontal velocity of your friend's. The vertical velocity will remain same. The resultant of the vertical and new horizontal velocity will give you the final answer of how you see your friend.  
Velocity of friend in horizontal direction will be $(v_2 \cos A)$
Velocity of friend in vertical direction will be $(v_2 \sin A)$
Horizontal Direction:
$ (v_2 \cos A -v_1) $  is the velocity of your friend in the horizontal direction relative to you.  
Vertical Direction:
$ (v_2 \sin A) $ is the velocity of your friend in the vertical direction relative to you.
Nothing changes as your entire velocity is in the horizontal direction.
Combining the two directions:
$ \sqrt{(v_2 \cos A -v_1)^2 + (v_2 \sin A)^2} $  is the velocity of your friend relative to you.
Method 2
The resultant vector of your friends velocity vector with the negative of your velocity vector
i.e. (Friends velocity vector) - (your velocity vector)
A: Using the notation that $\vec v_{\rm ab}$ is the velocity of $a$ relative to $b$ you need the velocity of $1$ relative to $2$ which is $$\vec v_{12} = \vec v_{1\rm g} +  \vec v_{\rm g 2} = \vec v_{1\rm g} -  \vec v_{\rm 2 g}$$  
which diagrammatically is as follows with $g$ as the ground.
 
It might help remember how to set out the vector addition by looking at the sequence of the subscript symbols 
$1\,2 = 1\,\mathbf{g} + \mathbf{g}\, 2$
