Addition of Vectors

Vector addition is a core concept in both physics and mathematics, vital for comprehending motion, forces, and numerous other phenomena. Unlike scalar quantities, which are characterized solely by magnitude (such as temperature or mass), vectors possess both magnitude and direction. This duality is crucial for accurately representing physical quantities like velocity, acceleration, and force. Mastering vector addition is essential for tackling problems in mechanics, electromagnetism, and various engineering disciplines.

1.0Addition of Two Vectors

Vectors possess both magnitude and direction, which means they cannot be added using standard arithmetic methods. Instead, they are combined geometrically. There are three fundamental laws of vector addition that can be applied.

1. Triangle Law of vector addition
2. Parallelogram Law of vector addition
3. Polygon Law of vector addition

2.0Graphical Methods(Triangle and Parallelogram Law)

1. Triangle Law of addition of two vectors

• If two vectors are depicted by two sides of a triangle in the same order then their sum or 'resultant vector' is given by the third side of the triangle taken in opposite order of the first two vectors.

• Shift one vector B ,without changing its direction, such that its tail coincides with the head of the other vector A . Now complete the triangle by drawing the third side, directed from tail of A  to head of B   (it is in opposite  order of A and  B vectors).
• Sum of two vectors is also termed as the resultant vector of these two vectors. 

Resultant R=A+B