ABCD is a quadrilateral. Find the sum of the vectors and

Given: ABCD is a quadrilateral as shown below

Consider ΔADC and apply triangle law of vector, we get

Similarly, consider ΔABC and apply triangle law of vector, we get

Substituting the value of from eqn(i) into eqn(ii), we get

Now add on both sides, we get

Hence sum of the vectors and is