Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of the vector a + b?

Apr 2, 2016

$| a + b | = 14.6$

Explanation:

Split up the two vectors into their $x$ and $y$ components and add them to their corresponding $x$'s or $y$'s, like so:

$3.3 x + - 17.8 x = - 14.5 x$
$- 6.4 y + 5.1 y = - 1.3 y$

Which gives a resultant vector of $- 14.5 x - 1.3 y$

To find the magnitude of this vector, use Pythagoras theorem. You can imagine the $x$ and $y$ components as perpendicular vectors, with a right angle where they join, and the $a + b$ vector, let's call it $c$, joining the two, and so $c$ is given by:

${c}^{2} = {x}^{2} + {y}^{2}$
$c = \sqrt{{x}^{2} + {y}^{2}}$

Substituting the values of $x$ and $y$,

$c = \sqrt{211.9}$
$c = 14.6$

which is the magnitude or length of the resultant vector.