vector expressed as This is known as the triangle law of vector addition. In general, if we have two vectors and (Fig . (i)), then to add them, they are positioned so that the initial point of one coincides with the terminal point of the other (Fig . (ii)).
Fig . (i) (iii) A C (ii) A C B B – –b C ’ Fig . For example, in Fig . (ii), we have shifted vector without changing its magnitude and direction, so that it’s initial point coincides with the terminal point of .
Then, the vector + , represented by the third side AC of the triangle ABC, gives us the sum (or resultant) of the vectors and i.e., in triangle ABC (Fig . (ii)), we have Now again, since , from the above equation, we have This means that when the sides of a triangle are taken in order, it leads to zero resultant as the initial and terminal points get coincided (Fig . (iii)). Now, construct a vector so that its magnitude is same as the vector , but the direction opposite to that of it (Fig .
(iii)), i.e., Then, on applying triangle law from the Fig . (iii), we have The vector is said to represent the difference of Now, consider a boat in a river going from one bank of the river to the other in a direction perpendicular to the flow of the river. Then, it is acted upon by two velocity vectors–one is the velocity imparted to the boat by its engine and other one is the velocity of the flow of river water. Under the simultaneous influence of these two velocities, the boat in actual starts travelling with a different velocity.
To have a precise idea about the effective speed and direction (i.e., the resultant velocity) of the boat, we have the following law of vector addition. If we have two vectors represented by the two adjacent sides of a parallelogram in magnitude and direction (Fig . ), then their sum is represented in magnitude and direction by the diagonal of the parallelogram