Question

Can the resultant of three vectors be zero?

Answer 1

In order to solve this problem you should have to know the concept of coplanar and just imagine three vectors and do some basic math operations ( addition(+) , subtraction(-) ). Then you will figure out something that will lead you to the answer of this question.

Complete answer:
Basically the resultant of three vectors will be zero if these three conditions are satisfied.
First of all we have to be familiar with the term coplanar. Coplanar stands for all the vectors that you are dealing with, they all have to lie on a single plane, in a three-dimensional space.
So, the first condition is “all three vectors are coplanar.”
Second condition “The sum ( resultant ) of any two of them is equal and opposite to the third one.” In other words, the direction of the resultant of any two vectors is exactly opposite to the direction of the third vector.
Let’s see one example of that. Consider a, b and c are the given three vectors.
Now, as second condition says,
$a + b = - c$ or $a + c = - b$ or $b + c = - a$.
Third condition “The magnitude of the resultant of two vectors is exactly equal to the magnitude of the third vector.”
Let’s see its example $|A| + |B| = |C|$ .

Note:
You can find coplanar by doing a scalar product of those three vectors. If the value of a scalar product is zero then they are coplanar. Three vectors are coplanar which means all three vectors are in the same plane. All three vectors form a triangle together which means they form three sides and three angles and three vertices.