# Converting a velocity vector into MPH?

I have a velocity vector on $X$, $Y$ and $Z$ axes. The values are represented as M/S (meters per second).

What algorithm should I use to convert this vector into a general MPH (miles per hour) value that takes into account all axes of the vector?

This may (or may not) be a very simple question. But I am far from being a genius at math! So apologies.

Thanks very much.

-

Multiply each coordinate by 2.23693629. In general, to convert units of a vector, you just convert units of each coordinate. This works because scalar multiplication by positive constants preserves direction, and because lengths of vectors and scalar multiplication are related by $\|c v\|=|c|\|v\|$. Scalar multiplication in this case just means multiplying each coordinate by the conversion factor.
For a vector with only an $x$ component, you just take the absolute value to get the length. For a vector with only $x$ and $y$ components, then using the Pythagorean theorem you can see that the length of the vector is the the square root of the sum of the squares of the components. With a slightly more elaborate picture you can apply the Pythagorean theorem again to get the same result in general, so you should have $2.2369\sqrt{v_x^2+v_y^2+v_z^2}$. – Jonas Meyer Nov 6 '10 at 19:51