problem 2.5 - express the force f in terms of x, y, and z components.

Explanation:

Step1: Recall force - component formula

$F_x = F\cos\alpha$, $F_y = F\cos\beta$, $F_z = F\cos\gamma$, where $\alpha$, $\beta$, $\gamma$ are the angles between the force vector and the $x$, $y$, $z$ - axes respectively.

Step2: Determine the angles

Given $F = 200$ lb, $\alpha=120^{\circ}$, $\beta = 45^{\circ}$, $\gamma = 60^{\circ}$.

Step3: Calculate the $x$ - component

$F_x=F\cos\alpha=200\cos120^{\circ}=200\times(-\frac{1}{2})=- 100$ lb.

Step4: Calculate the $y$ - component

$F_y=F\cos\beta=200\cos45^{\circ}=200\times\frac{\sqrt{2}}{2}=100\sqrt{2}$ lb.

Step5: Calculate the $z$ - component

$F_z=F\cos\gamma=200\cos60^{\circ}=200\times\frac{1}{2}=100$ lb.

Answer:

$F_x=-100$ lb, $F_y = 100\sqrt{2}$ lb, $F_z = 100$ lb