Addition Of Vectors

3. Addition of Vectors:

  Vectors are added in a particular way known as the triangle law. To see why this law is appropriate to add them this way consider the following example:

Example: The route taken by an automated vehicle An unmanned vehicle moves on tracks around a factory floor carrying components from the store at A to workers at C .

The vehicle may arrive at C either directly or via an intermediate point B. The movement from A to B can be represented by a displacement vector −→AB. Similarly, movement from B to C can be represented by the displacement vector −→BC, and movement from A to C can be represented by −→ AC. Since travelling from A to B and then B to C is equivalent to travelling directly from A to C we write −→ AB +−→ BC = −→ AC This is an example of the triangle law for adding vectors. Note that we can add vectors by placing the tail of the second at the head of the first and completing the third side of the triangle so formed. Suppose we wish to add b to a. To do this b is translated, keeping its direction and length unchanged, until its tail coincides with the head of a. Then the sum a + b is defined by the vector represented by the third side of the completed triangle, that is c, that we can write c = a + b since going along a and then along b is equivalent to going along c.

DRAW ADDITION OF VECTOR :