In vector addition, the sum of two (or more) vectors will give a resultant vector. There are a number of sites that will help you with tutorials. A link to one can be found below.
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The condition is the two vectors are perpendicular to each other.
Two vectors: no. Three vectors: yes.
Two vectors, no; three vectors yes.
No, the sum of two vectors cannot be equal to either of the vectors individually. In vector addition, the resultant vector is determined by the magnitude and direction of the individual vectors. The sum of two vectors represents the combination of their effects, resulting in a new vector with different properties than the original vectors.
You do vector addition.