# Given two vectors A = -1.00 î + 3.00j + 5.00k and B = 2.00j + 3.00 1.00 k, how can I find the magnitude of each vector and write an expression for the vector difference A-B, using init vectors?

## how can I find the magnitude of the vector difference A - B?

Jun 24, 2018

See solution below

#### Explanation:

$\vec{A} = - \hat{i} + 3 \hat{j} + 5 \hat{k}$

$\vec{B} = 2 \hat{i} + 3 \hat{j} + \hat{k}$

For value of $\vec{A}$ and $\vec{B}$ ,

$| \vec{A} | = \sqrt{{\left(- 1\right)}^{2} + {3}^{2} + {5}^{2}} = \sqrt{35}$

$| \vec{B} | = \sqrt{{\left(2\right)}^{2} + {3}^{2} + {1}^{2}} = \sqrt{14}$

For vector difference,
$\vec{A} - \vec{B} = \vec{R} = \left(- 1 - 2\right) \hat{i} + \left(3 - 3\right) \hat{j} + \left(5 - 1\right) \hat{k}$
$\Rightarrow \vec{R} = - 3 \hat{i} + 4 \hat{k}$

For its magnitude,
|vecR| = sqrt((-3)^2 + 4^2
$| \vec{R} | = 5$