Question

1. Using triangle method, determine the resultant of vectors:

A= 15 units 20 degrees SW
B= 20 units 50 degrees NW
2. Using parallelogram method, determine the resultant of vectors:
A= 100 units 40 degrees
NW B= 300 units 80 degrees NE
3. The equilibrant of vectors A=(-6,-2) is vector E. What is E?

Answer 1

With the graphical methods for the sum of vectors we can find the resulting sum vector.

a) see attached 1a4

b) see attached 1a6

c) the equilibrium vector is E = (6,2)

Vectors are magnitudes that in addition to having modulus also have direction, so the sum of them gives another vector that has modulus and direction, there are numerical and graphical methods for this process, for a large number of vectors the numerical method is easier , but for two or three vectors the graphical method can be applied.

Graphic method of the sum of vectors, this method is based on drawing the vectors and finding the resulting vector for a fixed coordinate system, it can be done in two ways:

• Triangle method consists of moving the second vector in parallel to the tip of the first veto and the resultant sees from the origin of the first vector to the tip of the last

• Parallelogram method in this procedure, all the vectors are translated in parallel until their origin touch, then parallel vectors are drawn at the tip of each vector, forming a parallelogram and the resulting vector goes from the origin of the vectors to their tip.

In the attached we can see the application of the two methods for the sum of the vectors a and b

1. Attachment A illustrates the triangle method, this is a schematic, for real measurements use squared paper

2. Attachment B shows the parallelogram method.

Two two methods can be used, but the analytical method despite being longer is more accurate.

to obtain the values ​​of the resultin, a y be should be used for the module and a protractor for the angles

.

the result of the sum applied the triangle method is

R = 28.6

tae = 20.9 NW

the result for the parallelogram method is

R = 360

yae = 86.2º NE

3. The equilibrium vector is in charge of balancing the system, it has the same magnitude as the resulting vector but with the opposite sign.

If the resulting vector is A = (-6, -2)

the equilibrium vector is E = (6,2)

In conclusion with the graphic methods for the sum of vectors we can find the resulting sum vector.

Learn more about vector addition here