# Math Help - quick vector problem

1. ## quick vector problem

Determine ||v+w|| if v and w are unit vectors separated by 0.3 radians

2. First thing to do is draw a diagram of the triangle. Two sides are 1 and the angle between them is $\pi-0.7$. Use cosine rule to find the distance required.

3. Originally Posted by casesam
Determine ||v+w|| if v and w are unit vectors separated by 0.3 radians
Let $\vec w = (1, 0)$

Since $|\vec w| = |\vec v|$ you can express $\vec v$ as:

$\vec v = |\vec w|(\cos(0.3), \sin(0.3))$

Therefore

$\vec v + \vec w = |\vec w|(1+\cos(0.3), \sin(0.3))$

Now calculate

$|\vec v + \vec w| = |\vec w|\sqrt{(1+\cos(0.3))^2+(\sin(0.3))^2}\approx 1.9778$ because $|\vec w| = 1$.