#vectorquantity #vectortriangle #vectoraddition #textbook #physics

Ch:- 3

Pg:- 59,60

Vector addition is a fundamental process used to combine two or more vectors to produce a resultant vector. A common graphical method of representing vector addition is through a vector triangle. This method is particularly useful when dealing with vectors that are not aligned along the same direction.

1. Vector Addition (Concept):

Vectors are quantities that have both magnitude (size) and direction. When adding vectors, both of these attributes must be considered. The two primary methods for vector addition are:

• Graphical Addition: Using diagrams like the vector triangle.

• Analytical Addition: Breaking the vectors into components and adding them mathematically.

2. Vector Triangle Method:

The vector triangle method is a graphical way to add two vectors. In this method, the vectors are arranged tip-to-tail, meaning the head (arrow) of the first vector is connected to the tail (base) of the second vector. The resultant vector is the one that closes the triangle by connecting the tail of the first vector to the head of the last.

Here are the steps involved:

Steps for the Vector Triangle Method:

1. Draw the first vector to scale in the correct direction. This vector will serve as one side of the triangle.

2. Draw the second vector starting from the head (arrow) of the first vector, again keeping it to scale and in the correct direction. This forms the second side of the triangle.

3. Draw the resultant vector, which connects the tail of the first vector to the head of the second vector. This forms the third side of the triangle.

4. The length of the resultant vector represents the magnitude, and the angle it makes with a reference axis gives its direction.

3. Parallelogram Law of Vector Addition:

Another graphical method of vector addition is the parallelogram law, which is closely related to the vector triangle method. When two vectors are placed tail-to-tail, they form adjacent sides of a parallelogram. The resultant vector is the diagonal of the parallelogram, starting from the common tail.