Chapter 9.4, Problem 32AYU

In Problems 29-36, the vector $\text{v}$ has initial point $p$ and terminal point $Q$. Write $\text{v}$ in the form $ai+bj$; that is, find its position vector.

$P=\left(-1,4\right);Q=\left(6,2\right)$

To determine

To find: The position vector in the form of $ai+bj$.

Answer to Problem 32AYU

Solution:

$v=7i-2j$

Explanation of Solution

Given:

$P=\left(-1,4\right);Q=\left(6,2\right)$

Calculation:

If $v$ is a vector with initial point $\left(x_1,y_1\right)$ and terminal point $\left(x_2,y_2\right)$, then the following is the position vector $v=\langle x_2-x_1,y_2-y_1\rangle$.

Here $x_1=-1;y_1=4;x_2=6;y_2=2$,

$v=\langle x_2-x_1,y_2-y_1\rangle =\langle 6-\left(-1\right),2-4\rangle =\langle 7,-2\rangle$

$v=\langle 7,-2\rangle =7\langle 1,0\rangle -2\langle 0,1\rangle =7i-2j$