Vectors

Adding Vectors (Finding the Resultant)

• When two forces or velocities act on an object simultaneously, their combined effect is called the Resultant
• if exam asks to find resultant, even when using calculation method, vector diagram has to be drawn

Diagram method

To add Vector A and Vector B:

1. Draw Vector A
2. Start Vector B from the tip (arrowhead) of Vector A
3. The Resultant connects end of B to the start of A
   • Resultant has to be drawn with double arrow, vectors a and b draw with single arrow

Calculation method

If the triangle is not a right-angled triangle, use the Cosine Rule. $R = \sqrt{A^2 + B^2 - 2AB \cos \theta}$ else use Pythagoras theorem $a^2 + b^2 = c^2$

Equilibrium (Closed Vector Triangles)

When three coplanar forces act on an object in equilibrium, their vectors form a closed triangle when drawn head-to-tail, meaning net force and acceleration is 0

Formulas