Answer
\[
a) \langle 2,1\rangle
\]
\[
b) \langle-1,6,1\rangle
\]
\[
c\langle-5,0,0\rangle
\]
Work Step by Step
The components of a vector $\overrightarrow{P_{1} P_{2}}$ with start point $P_{2}(c, d)$ , 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 $P_{2}(-4,-1)$ and $P_{1}(-6,-2)$
\[
\overrightarrow{P_{1} P_{2}}=\langle-4-(-6),-1-(-2)\rangle=\langle 2,1\rangle
\]
b) For $P_{2}(-1,6,1)$ and $P_{1}(0,0,0)$
\[
\overrightarrow{P_{1} P_{2}}=\langle-1-0,6-0,1-0\rangle=\langle-1,6,1\rangle
\]
c) For $P_{2}(9,1,-3)$ and $P_{1}(4,1,-3)$
\[
\overrightarrow{P_{1} P_{2}}=\langle9-4,1-1,-3-(-3)\rangle=\langle-5,0,0\rangle
\]
