Question

Which pair of vectors below, if summed, would create a state of equilibrium (a resultant of 0i + 0j)?

a. 0i + 0j and 2i − 2j

b. 2i + 2j and 2i − 2j

c. 2i + 2j and -2i − 2j

d. 2i + 0j and 0i + 2j

Answer 1

2i + 2j and -2i − 2j

Step-by-step explanation:

Answer 2

Right answer: 2i + 2j and -2i − 2j

The coordinates of a resulting vector are calculated by algebraically adding the respective components of the vectors.

In other words: to sum two vectors we only have to sum, respectively, the components i and the components j of each vector.

For example, the pair of vectors 2i + 2j and -2i − 2j:

2i + (-2i) = 0i

and

2j + (-2j) = 0j

Then, the resultant is:

0i + 0j

Therefore, the correct option is c.

If we try with the other options, the resultant will not be 0i + 0j:

a. 0i + 0j and 2i − 2j:

2i-2j

b. 2i + 2j and 2i − 2j:

4i-0j

d. 2i + 0j and 0i + 2j:

2i+2j