Answer to Question #250191 in Vector Calculus for weiou

Question #250191

 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
2021-10-13T07:41:09-0400
"\\vec F = 1200\ud835\udc22 + 800\ud835\udc23 \u2212 1500\ud835\udc24"

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

"\\alpha=\\cos^{-1}\\bigg(\\dfrac{F_x}{|\\vec F|}\\bigg)=\\cos^{-1}\\bigg(\\dfrac{1200}{100\\sqrt{433}}\\bigg)\\approx54.78\\degree"

"\\beta=\\cos^{-1}\\bigg(\\dfrac{F_y}{|\\vec F|}\\bigg)=\\cos^{-1}\\bigg(\\dfrac{800}{100\\sqrt{433}}\\bigg)\\approx67.39\\degree"

"\\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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