Direction Angle

radians

degrees

$\mathrm{\α}\=\arccos \left(1\/\sqrt{14}\right)$

$1.3002$

$74.5°$

$\mathrm{\β}\=\arccos \left(2\/\sqrt{14}\right)$

$1.0068$

$57.7°$

$\mathrm{\γ}\=\arccos \left(3\/\sqrt{14}\right)$

$0.64048$

$36.7°$

Table 1.1.8(a)   Direction angles for given vector

Loading Student:-MultivariateCalculus

Angle $\mathrm{\α}$ 

$⟨1\,2\,3⟩\,⟨1\,0\,0⟩$ = $\stackrel{\text{angle}}{\to }$$\arccos \left(\frac{1}{14}\sqrt{14}\right)$$\stackrel{\text{at 5 digits}}{\to }$$1.3002$

Angle $\mathrm{\β}$ 

$⟨1\,2\,3⟩\,⟨0\,1\,0⟩$ = $\stackrel{\text{angle}}{\to }$$\arccos \left(\frac{1}{7}\sqrt{14}\right)$$\stackrel{\text{at 5 digits}}{\to }$$1.0068$

Angle $\mathrm{\γ}$ 

$⟨1\,2\,3⟩\,⟨0\,0\,1⟩$ = $\stackrel{\text{angle}}{\to }$$\arccos \left(\frac{3}{14}\sqrt{14}\right)$$\stackrel{\text{at 5 digits}}{\to }$$0.64048$

$\mathrm{Student}:-\mathrm{MultivariateCalculus}:-\mathrm{Angle}\left(⟨1\,2\,3⟩\,⟨1\,0\,0⟩\right)$ = $\arccos \left(\frac{1}{14}\sqrt{14}\right)$$$

$\mathrm{Student}:-\mathrm{MultivariateCalculus}:-\mathrm{Angle}\left(⟨1\,2\,3⟩\,⟨0\,1\,0⟩\right)$ = $\arccos \left(\frac{1}{7}\sqrt{14}\right)$$$

$\mathrm{Student}:-\mathrm{MultivariateCalculus}:-\mathrm{Angle}\left(⟨1\,2\,3⟩\,⟨0\,0\,1⟩\right)$ = $\arccos \left(\frac{3}{14}\sqrt{14}\right)$$$