Given 2 vectors A = 4.00i + 3.00j  and B =5.00i - 2.00 j how do you find the magnitude & direction of the vector difference A - B?

Jan 24, 2016

We can subtract directly the corresponding components and check using the parallelogram rule.

Explanation:

Have a look:

Where, graphically, I used the fact that:
$\vec{A} - \vec{B} = \vec{A} + \left(- \vec{B}\right)$

For the magnitude we use Pythagoras (with the components) to get:
$| \vec{A} - \vec{B} | = \sqrt{{\left(- 1\right)}^{2} + {\left(5\right)}^{2}} = \sqrt{1 + 25} = \sqrt{26} \approx 5.1$

For the direction I can see that will be ${90}^{\circ}$ from the $x$ axis up to the $y$ axis, plus the little bit passed the $y$ axis given as:
$\theta = \arctan \left(\frac{1}{5}\right) = {11.3}^{\circ}$
giving in total: angle$= {90}^{\circ} + {11.3}^{\circ} = {101.3}^{\circ}$