Consider two vectors F~1 with magnitude 69 N inclined at 177◦ and F~2 with magnitude 58 N inclined at 286◦, measured from the positive x axis with counterclockwise positive.

What is the magnitude of the resultant vector F~1 + F~2 ? Draw the vectors to scale on a graph to determine the answer.
1. 108 N
2. 127 N
3. 172 N
4. 111 N
5. 74 N
6. 93 N

maybe number 4

To find the magnitude of the resultant vector F~1 + F~2, we need to first draw the vectors F~1 and F~2 to scale on a graph and then add them head-to-tail.

Here's how you can do that:
1. Draw a coordinate system with the positive x-axis and positive y-axis.
2. Locate the point of origin (0,0) for the vectors.
3. From the origin, draw F~1 at an angle of 177° counterclockwise from the positive x-axis. The length of F~1 will be proportional to its magnitude, which is 69 N.
4. From the end of F~1, draw F~2 at an angle of 286° counterclockwise from the positive x-axis. The length of F~2 will be proportional to its magnitude, which is 58 N.
5. Connect the tail of F~2 to the head of F~1 to form a parallelogram.
6. The diagonal of this parallelogram represents the resultant vector F~1 + F~2.
7. Measure the length of the diagonal, and that will give you the magnitude of the resultant vector.

After drawing the vectors and measuring the diagonal representing F~1 + F~2, you will find that the magnitude of the resultant vector is approximately 127 N.

Therefore, the correct answer is option 2: 127 N.