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 a?

Jan 28, 2016

The magnitude (length) of a vector in two dimensions is given by:

$l = \sqrt{{a}^{2} + {b}^{2}}$. In this case, for the vector $a$, $l = \sqrt{{3.3}^{2} + {\left(- 6.4\right)}^{2}} = \sqrt{51.85} = 7.2 u n i t s .$

Explanation:

To find the length of a vector in two dimensions, if the coefficients are $a$ and $b$, we use:

$l = \sqrt{{a}^{2} + {b}^{2}}$

This might be vectors of the form $\left(a x + b y\right) \mathmr{and} \left(a i + b j\right) \mathmr{and} \left(a , b\right)$.

Interesting side note: for a vector in 3 dimensions, e.g. $\left(a x + b y + c z\right)$, it's

$l = \sqrt{{a}^{2} + {b}^{2} + {c}^{2}}$ - still a square root, not a cube root.

In this case, the coefficients are $a = 3.3$ and $b = - 6.4$ (note the sign), so:

$l = \sqrt{{3.3}^{2} + {\left(- 6.4\right)}^{2}} = \sqrt{51.85} = 7.2$ $u n i t s$