Final answer:
To find the angles of vectors A-G, apply vector addition using trigonometry to determine components and resultant vector, then measure with a protractor or calculate via trigonometric relationships for the resultant angle.
Step-by-step explanation:
To find the measure of the angles for the vectors A-G as requested, we will use analytical methods involving trigonometry and vector addition. For the vector G given by G = A + 2B - F, you'll need to find the components of each individual vector with the formulas Ax = A cos(\(\alpha\)) and Ay = A sin(\(\alpha\)) where \(\alpha\) is the direction angle with the horizontal.
Once you have the components, add them together following the vector equation to find the components of the resultant vector G. Use the Pythagorean theorem to find the resultant magnitude: G = \(\sqrt{Gx^2 + Gy^2}\) and use trigonometric relationships to calculate the direction angle \(\theta G\).
If using graphical methods, attach a protractor to figure 2.13, scale your vectors accordingly, and construct a parallelogram as suggested in the illustration from the material where the resultant vector R can be obtained by measuring the diagonal.