Chapter 9.4, Problem 29AYU

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.

$P=\left(3,\text{2}\right);Q=\left(5,6\right)$

To determine

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

Answer to Problem 29AYU

Solution:

$v=2i+4j$

Explanation of Solution

Given:

$P=\left(3,2\right);Q=\left(5,6\right)$

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 $x_1=3;y_1=2;x_2=5;y_2=6$,

$v=\langle x_2-x_1,y_2-y_1\rangle =\langle 5-3,6-2\rangle =\langle 2,4\rangle$

$v=\langle 2,4\rangle =2\langle 1,0\rangle +4\langle 0,1\rangle =2i+4j$