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.

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.

asked 2021-02-17
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.

Answers (1)

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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