A vector is a physical quantity that has both a magnitude (size) and a specific direction. While scalar numbers like time or mass can be added normally, vectors require special rules because direction matters.

Graphical Addition: The Head-to-Tail Method

The easiest way to add two vectors is the 'head-to-tail' method. You draw the first vector as an arrow. Then, you place the starting point (tail) of the second vector at the end point (head) of the first. The result, called the resultant vector, is a new arrow drawn from the very start to the final tip. For example, if you walk 3 meters East and then 4 meters North, your resultant displacement is 5 meters North-East, following a right-angled triangle pattern.

Analytical Addition: Components

Analytical addition uses math instead of drawings. Every vector can be broken into horizontal (x) and vertical (y) parts, called components. To add two vectors, you add their x-parts together and their y-parts together. If Vector A is (2, 3) and Vector B is (4, 1), the resultant vector is (2+4, 3+1), which equals (6, 4). This method is much more accurate than drawing on paper.

Subtraction of Vectors

Subtracting vectors is actually the same as adding a negative vector. A negative vector has the same size but points in the exact opposite direction. To calculate A minus B, you simply flip the direction of B and add it to A. If B is pointing North, negative B points South. Adding this reversed vector follows the exact same 'head-to-tail' or component rules used in addition.

Key Formulas

• Resultant Magnitude: Using the Pythagorean theorem, the magnitude of a resultant vector is √ (x² + y²).
• Direction: The angle θ can be found using the formula tan θ = (vertical component / horizontal component).
• Vector Addition Rule: R = A + B means adding corresponding components: R_x = A_x + B_x and R_y = A_y + B_y.