# The x and y components of a vector r are r_x=14 m and r_y=-95 m respectively. Find the direction and the magnitude of the vector r.

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The x and y components of a vector r are $$\displaystyle{r}_{{x}}={14}$$ m and $$\displaystyle{r}_{{y}}=-{95}$$ m respectively. Find the direction and the magnitude of the vector r.

2021-02-19
Magnitude of $$\displaystyle{r}=\sqrt{{{{r}_{{x}}^{{2}}}+{{r}_{{y}}^{{2}}}}}={\left[{\left({142}+{\left(-{95}\right)}{2}\right]}^{{{\frac{{{1}}}{{{2}}}}}}={96.02}{m}\right.}$$
Direction Angle $$\displaystyle={{\tan}^{{-{1}}}{\frac{{{r}_{{y}}}}{{{r}_{{x}}}}}}={{\tan}^{{-{1}}}{\frac{{-{95}}}{{{14}}}}}=-{81.61}$$

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