magine a $3-$dimensional world with coordinates that are labeled with x$,$ y$,$ and z$,$ as if you are in a large room with walls, a high ceiling and a floor. The edges are x$,$ y and z with z up toward the ceiling, the flat plane floor is x$-$y$.$

Starting at the origin, go along $"$x$"5$ meters. Then go parallel to $"$y$"6$ meters. Then go up parallel to $"$z$"4$ meters. This point is somewhere in the room above the floor.

What is the vector from the origin to the point?

What is the magnitude of that vector? That is$,$ what is its length?

What angle does it make to the floor? This would be $90\backslash$deg $-\backslash$theta where $\backslash$theta is the angle down from the z axis. $($Hint: Use z and the length of the vector to find the angle from trigonometry. $)$

If you dropped from that point directly down to the floor, how far would you fall?

How long would it take, given that falling objects accelerate at $9\mathrm{.}8$ m$/$s every second $(9\mathrm{.}8$ m$/$s$2)?$ You could round this to $10$ m$/$s$2$ to make the math easier.