Question

What is the speed of an object that travels from `( 4,-2,2)` to `( -3, 8,-7 )` over `3 s`?

Answer 1

The answer would be the distance between the two points (or vectors) divided by the time. So you should get `(sqrt(230))/3` units per second.

Explanation:

To get the distance between the two points (or vectors), just use the distance formula `d = sqrt(x^2 +y^2 +z^2)` on the difference between the two given points.

ie `(x,y,z) = (-3-4, 8 -(-2),-7-2) = (-7,10,-9)` ( note : it does not matter which way around we substract the points since the formula uses squares and thus eliminates any negative signs. We can do point A - point B or point B - point A)

Now applying the distance formula, we get
`d = sqrt((-7)^2 +(10)^2 +(-9)^2) = sqrt(230)`

Then all that is left is to divide by the time to get the answer.

Interesting fact: This distance formula is actually called the Euclidean Norm in the real normed space `R^n`, denoted by `||\bar(x)||_2`.