Using GRAPHICAL METHOD, find the vector sum of a force of 20 N directed 60 degrees east of north and a force of 60 N directed west? Please show all steps and equations used.

Fr = 20N[30oCCW] + 60N[180oCCW] = Resultant force.

X = 20*Cos30 + 60*Cos180 = 17.3 - 60 = -42.7 N.
Y = 20*sin30 + 60*sin180 = 10 + 0 = 10 N.

Tan A = Y/X = 10/-42.7 = -0.23419.
A = -13.2o = 76.8o W. of N. = Direction.

Fr = sqrt(X^2 + Y^2) =

Note: This not a graphical method.

To find the vector sum of the two forces using the graphical method, we will visually represent the two forces as vectors on a graph and then combine them to find the resultant vector.

Step 1: Draw a coordinate system or simply a set of axes on a piece of paper. Label the x-axis as East-West and the y-axis as North-South.

Step 2: Draw an arrow to represent the first force of 20 N directed 60 degrees east of north. To do this, start at the origin (0, 0) and draw an arrow 60 degrees above the positive x-axis with a length of 20 units.

Step 3: Draw an arrow to represent the second force of 60 N directed west. To do this, start at the origin (0, 0) and draw an arrow to the left along the negative x-axis with a length of 60 units.

Step 4: Extend the arrow representing the second force in the opposite direction.

Step 5: Complete the parallelogram by drawing lines from the ends of each arrow to their respective opposite ends, creating a parallelogram.

Step 6: Draw the diagonal of the parallelogram to represent the resultant vector. This diagonal represents the vector sum of the two forces.

Step 7: Measure the length of the resultant vector and its direction relative to the positive x-axis.

Step 8: If needed, convert the length of the resultant vector from units on the graph to units of newtons (N).

By following these steps and considering the lengths and angles of the forces, you should be able to graphically determine the vector sum of the two forces.