Answer
a) $\overrightarrow{P_{1} P_{2}}=\langle-1,3\rangle$
b) $\overrightarrow{P_{1} P_{2}}=\langle-7,2\rangle$
c) $\overrightarrow{P_{1} P_{2}}=\langle-3,6,1\rangle$
Work Step by Step
The components of a vector $\overrightarrow{P_{1} P_{2}}$ with start point $P_{2}(c, d)$ and end point $P_{1}(a, b)$ are:
\[
\overrightarrow{P_{1} P_{2}}=-\langle a, b\rangle+\langle c, d\rangle=\langle c-a, d-b\rangle
\]
a) For $P_{2}(2,8)$ and $P_{1}(3,5)$
\[
\overrightarrow{P_{1} P_{2}}=\langle 2-3,8-5\rangle=\langle-1,3\rangle
\]
b) For $P_{2}(0,0)$ and $P_{1}(7,-2)$
\[
\overrightarrow{P_{1} P_{2}}=\langle 0-7,0-(-2)\rangle=\langle-7,2\rangle
\]
c) For $P_{2}(2,4,2)$ and $P_{1}(5,-2,1)$
\[
\overrightarrow{P_{1} P_{2}}=\langle 2-5,4-(-2), 2-1\rangle=\langle-3,6,1\rangle
\]
