Finding a Position Vector

Find the unique position vector \(\mathbf{v}\) of a vector whose initial point is \(P_{1}\) and whose terminal point is \(P_{2}.\)

1. \(P_{1}=(-1,2),\quad P_{2}=(4,6)\)
2. \(P_{1}=(3,4,2),\quad P_{2}=(7,-8,5)\)

Solution To find \(\mathbf{v}\), subtract corresponding components.

1. Then \(\mathbf{v}=\langle 4-(-1), 6-2\rangle =\langle 5,4\rangle \), as shown in Figure 27.
2. Here, \(\mathbf{v}=\langle 7-3,-8-4,5-2\rangle =\langle 4,-12,3\rangle\)