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find-the-magnitude-and-direction-of-the-vector-r-3i-4j-to-the-nearest-degree-a-7N-143-0-b-5N-143-0-c-5N-127-0-d-7N-127-0-




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

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