# Vector A has a magnitude of 10 and points in the positive x-direction. Vector B has a magnitude of 15 and make an angle of 34 degrees with the positive x-axis. What is the magnitude of A - B?

Apr 24, 2016

$8.7343$ units.

#### Explanation:

$A - B = A + \left(- B\right)$

$= 10 \angle {0}^{\circ} - 15 \angle {34}^{\circ}$

$= \sqrt{{\left(10 - 15 \cos {34}^{\circ}\right)}^{2} + {\left(15 \sin {34}^{\circ}\right)}^{2}} \angle {\tan}^{- 1} \left(\frac{- 15 \sin {34}^{\circ}}{10 - 15 \cos {34}^{\circ}}\right)$

$= 8.7343 \angle {73.808}^{\circ}$.

Hence the magnitude only is $8.7343$ units.