The angle between vectors a and b is 45. If |a| =5 units and |b| =4 units, find the value of |a-b| and of |a+b|
Think of $\displaystyle \vec{a}~\&~\vec{b}$ as adjacent sides of a parallelogram.
Then $\displaystyle \vec{a}-\vec{b}$ is the diagonal opposite the angle between them.
$\displaystyle \vec{a}+\vec{b}$ is the diagonal opposite the angle adjacent to the angle between them.
Now use the law of cosines.
I hope that you know that $\displaystyle |a- b|^2= |a|^2- 2a\cdot b+ |b|^2$ and $\displaystyle |a+ b|^2= |a|^2+ 2a\cdot b+ |b|^2$.
And you should know that $\displaystyle a\cdot b= |a||b|cos(\theta)$ where $\displaystyle \theta$ is the angle between a and b.
I see Plato got in just ahead of me. Different points of view about the same thing.