# Vector A points to the north and has length A. Vector B points to the east and has length B=2.0A. How do you find the magnitude of C=3.6A+B in terms of A?

Apr 11, 2018

The answer is $= 4.12 A$

#### Explanation:

The vectors are the following :

$\vec{A} = < 0 , 1 > A$

$\vec{B} = < 2 , 0 > A$

$\vec{C} = 3.6 \vec{A} + \vec{B}$

$= \left(3.6 \times < 0 , 1 >\right) A + < 2 , 0 > A$

$= < 2 , 3.6 > A$

The magnitude of $\vec{C}$ is

$= | | \vec{C} | | = | | < 2 , 3.6 > | | A$

$= \sqrt{{2}^{2} + {3.6}^{2}} A$

$= 4.12 A$