This law is known as the associative law of vector addition. Now, Applying the triangle law of vector addition to the Δ OAC, we have Then the vector joining the tail of the first vector and the head of the second vector represents the resultant completely i.e.Thus the tail of the second vector lies at the head of the first vector. Then from the head of the first vector, the second vector is drawn with the same scale and in the same direction of the second vector.The first vector is drawn with a suitable scale and in the given direction.Consider two vectors which are to be added as shown.When two vectors which are to be added taken in order are represented in direction and magnitude by two sides of a triangle then the third side taken in opposite order represents the resultant completely i.e. mass can be added to mass and time can be added to time, but the mass cannot be added to the time. The two scalars to be added should have the same nature.force can be added to force and velocity can be added to velocity, but the force cannot be added to the velocity. The two vectors to be added should have the same nature. A resultant vector is defined as a single vector whose effect is the same as the combined effect of two or more vectors.
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