I'm having trouble with this question:
Find the distance d between the points $P_1 = (-2, -9, -8)$ and $P_2 = (-3,5,-2)$ by first finding the vector $v$ from $P_1$ to $P_2$, then finding the length of $v$. Use the square root symbol where needed to give an exact answer.
Now I know that typically you would use the formula to find the euclidean distance between points in three dimensions (which I cant post here because its giving me issues), but the fact that it asks to first find vector $v$ then its length is making me confused.
What do I do?
Best Answer
The vector from $P_1$ to $P_2$ is
$\begin{pmatrix} -3\\5\\-2 \end{pmatrix} - \begin{pmatrix} -2\\-9\\-8 \end{pmatrix} = \begin{pmatrix} -1\\14\\6 \end{pmatrix},$
and the length of this vector is the distance between $P_1$ and $P_2$, which is
$\sqrt{(-1)^2 + 14^2 + 6^2} = \sqrt{233}$.