Question Number 132116 by aurpeyz last updated on 11/Feb/21
$${find}\:{the}\:{magnitude}\:{and}\:{direction}\:{of} \\ $$$${the}\:{vector}\:{r}=\mathrm{3}{i}−\mathrm{4}{j}\:{to}\:{the}\:{nearest}\: \\ $$$${degree} \\ $$$$\left({a}\right)\:\mathrm{7}{N}\:\mathrm{143}^{\mathrm{0}} \:\left({b}\right)\:\mathrm{5}{N}\:\mathrm{143}^{\mathrm{0}} \:\left({c}\right)\:\mathrm{5}{N}\:\mathrm{127}^{\mathrm{0}} \\ $$$$\left({d}\right)\:\mathrm{7}{N}\:\mathrm{127}^{\mathrm{0}} \\ $$
Answered by Olaf last updated on 11/Feb/21
![∣r∣ = (√(3^2 +(−4)^2 )) = 5 argr = arctan(−(4/3)) ≈ −53° = 127° [180] ⇒ (c)](Q132154.png)
$$\mid{r}\mid\:=\:\sqrt{\mathrm{3}^{\mathrm{2}} +\left(−\mathrm{4}\right)^{\mathrm{2}} }\:=\:\mathrm{5} \\ $$$$\mathrm{arg}{r}\:=\:\mathrm{arctan}\left(−\frac{\mathrm{4}}{\mathrm{3}}\right)\:\approx\:−\mathrm{53}°\:=\:\mathrm{127}°\:\left[\mathrm{180}\right] \\ $$$$\Rightarrow\:\left({c}\right) \\ $$
Commented by aurpeyz last updated on 20/Mar/21
![what does 127^0 [180] means? i thought it should be 270+47=317^0](Q136292.png)
$${what}\:{does}\:\mathrm{127}^{\mathrm{0}} \left[\mathrm{180}\right]\:{means}? \\ $$$${i}\:{thought}\:{it}\:{should}\:{be}\:\mathrm{270}+\mathrm{47}=\mathrm{317}^{\mathrm{0}} \\ $$