Triangle Law of Vector Addition

Consider the vectors given in the figure above. The line PQ represents the vector “p”, and QR represents the vector “q”. The line QR represents the resultant vector. The direction of AC is from A to C.  

Line AC represents, 

�⃗+�⃗p​+q​

The magnitude of the resultant vector is given by, 

∣�∣2+∣�∣2+2∣�∣∣�∣���(�)∣p∣2+∣q∣2+2∣p∣∣q∣cos(θ)​

θ represents the angle between the two vectors. Let φ be the angle made by the resultant vector with the vector p.

���(�)=�sin⁡��+�cos⁡�tan(ϕ)=p+qcosθqsinθ​

The above formula is known as the Triangle Law of Vector Addition.