Onur is floating freely in outer space with a propulsion thruster to help him counteract the pull of gravity. The gravitational forces pulling on his body are negligible except for those from the nearest planet (described by force vector $\purple{\vec p}\,$) and the nearest star (described by force vector $\blue{\vec s}\,$). Onur, the planet, and the star are in the same plane, so we can describe the gravitational forces as two-dimensional vectors.
$\quad$$\purple{\vec{p}} = (4,6)$
$\quad$$\blue{\vec{s}} = (1,7)$
$\quad$(Forces are given in newtons, $\text{N}$.)
**Assuming Onur wants the net gravitational force pulling on his body to be zero, with what force should he engage his propulsion thruster?**
[[☃ numeric-input 1]]$\,\text{N}$
(Round your final answer to the nearest tenth.)
**At what angle should Onur's propulsion thruster exert force? Assume $0$ is the rightward direction.**
[[☃ numeric-input 2]] $\text{rad}$
(Round your final answer to the nearest tenth. Your answer should be between $0$ and $2\pi$.)
