Re: How to find unit vector

Quote:

Originally Posted by

**daigo** But if I forgot that I had to divide the components by the magnitude, I would not know how to get the unit vector. So I guess I am asking why you divide the components by the magnitude in order to get the unit vector?

**Unit vector** means a vector of **length 1**. That is why.

Re: How to find unit vector

If the vector is <a, b> then its length is, as you say, $\displaystyle \sqrt{a^2+ b^2$. If you multiply the entire vector, and so each component, by that, you have

$\displaystyle \left<\frac{a}{\sqrt{a^2+b^2}}, \frac{b}{\sqrt{a^2+ b^2}}\right>$ and **its** length is

$\displaystyle \sqrt{\left(\frac{a}{\sqrt{a^2+ b^2}}\right)^2+ \left(\frac{b}{\sqrt{a^2+ b^2}}\right)^2}= \sqrt{\frac{a^2}{a^2+ b^2}+ \frac{b^2}{a^2+ b^2}}$

$\displaystyle = \sqrt{\frac{a^2+ b^2}{a^2+ b^2}}= 1$