Question

 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.

Answer 1

$$\vec F = 1200𝐢 + 800𝐣 − 1500𝐤$$

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

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

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

$$\gamma=\cos^{-1}\bigg(\dfrac{F_z}{|\vec F|}\bigg)=\cos^{-1}\bigg(\dfrac{-1500}{100\sqrt{433}}\bigg)\approx136.125\degree$$