**Introduction to rectangular component method**

Rectangular component method of addition of vectors is the simplest method to add a number of vectors acting in different directions.

**Details of method**

Consider two vectors:

making angles q1 and q2 with +ve x-axis respectively.

**Step 1:**

**Step 2:**

**Step 3:**

Representative lines of v1 and v2 are OA and OB respectively. Join O and B which is equal to resultant vector of v1 and v2.

**Step 4:**

Resultant vector along X-axis can be determined as:

**Step 5:**

Resultant vector along Y-axis can be determined as:

**Step 6:**

Now we will determine the magnitude of resultant vector.

In the right angled triangle DBOD:

**Step 7:**

Finally, the direction of resultant vector will be determined.

Again in the right angled triangle DBOD:

Where q is the angle that the resultant vector makes with the positive X-axis.

In this way we can add a number of vectors in a very easy manner.

This method is known as addition of vectors by rectangular components method.

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