Question #250863

find the angles between the force f = 1200𝐢 + 800𝐣 − 1500𝐤 n and the x-, y-, and z-axes. show your results on a sketch of the coordinate system.


1
Expert's answer
2021-10-14T11:08:28-0400




F=1200𝐢+800𝐣1500𝐤\vec F = 1200𝐢 + 800𝐣 − 1500𝐤

F=(1200)2+(800)2+(1500)2=100433(N)|\vec F|=\sqrt{(1200)^2+(800)^2+(-1500)^2}=100\sqrt{433}(N)

α=cos1(FxF)=cos1(1200100433)54.78°\alpha=\cos^{-1}\bigg(\dfrac{F_x}{|\vec F|}\bigg)=\cos^{-1}\bigg(\dfrac{1200}{100\sqrt{433}}\bigg)\approx54.78\degree

β=cos1(FyF)=cos1(800100433)67.39°\beta=\cos^{-1}\bigg(\dfrac{F_y}{|\vec F|}\bigg)=\cos^{-1}\bigg(\dfrac{800}{100\sqrt{433}}\bigg)\approx67.39\degree

γ=cos1(FzF)=cos1(1500100433)136.125°\gamma=\cos^{-1}\bigg(\dfrac{F_z}{|\vec F|}\bigg)=\cos^{-1}\bigg(\dfrac{-1500}{100\sqrt{433}}\bigg)\approx136.125\degree


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