F1=90N x=3/5 y=0 z=4/5 F2=150N x=45 y=45 z=60 F3=200N x=0 y=0 z=90 find the resultant of Fr. Fun dalpha betta and gamma

To find the resultant force \( \mathbf{F}_r \) and its direction cosines (\(\alpha, \beta, \gamma\)), we first need to break down each force vector into its components along the x, y, and z axes. 

### Step 1: Calculate Components of Each Force

Given forces:
1. \( F_1 = 90 \, \text{N} \), \( x = \frac{3}{5} \), \( y = 0 \), \( z = \frac{4}{5} \)
2. \( F_2 = 150 \, \text{N} \), \( x = 45^\circ \), \( y = 45^\circ \), \( z = 60^\circ \)
3. \( F_3 = 200 \, \text{N} \), \( x = 

Learn how to calculate the resultant force and direction cosines from given force vectors, including detailed component breakdowns and calculations. This problem involves force vector components along different axes and requires understanding of vector addition techniques.

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