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Q. 30

Expert-verified
Found in: Page 603

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problem, the vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.

$v=\left(9,3\right)\phantom{\rule{0ex}{0ex}}Positionvector\left(9i+3j\right)$

See the step by step solution

## Step1. Given Information

Initial point P$\left(-3,2\right)$

Terminal point Q$\left(6,5\right)$

We know that if P$\left({x}_{1},{y}_{1}\right)$ is the initial point and Q$\left({x}_{2,}{y}_{2}\right)$is the terminal point then the position vector is

$v=\left(\left({x}_{2}-{x}_{1}\right),\left({y}_{2}-{y}_{1}\right)\right)$

## Step 2. Calculating the position vector

$v=\left(\left({x}_{2}-{x}_{1}\right),\left({y}_{2}-{y}_{1}\right)\right)$

for P (-3,2)

and Q (6,5)

$v=\left(\left(6-\left(-3\right)\right),\left(5-2\right)\right)\phantom{\rule{0ex}{0ex}}v=\left(9,3\right)$

in vector form $v=9i+3j$