Objective

To verify the distributive property of vector multiplication, c⃗ x (a⃗+b⃗)= I c⃗ x a⃗ I + I c⃗ x b⃗ I.

Prerequisite knowledge

• Formula for the area of a parallelogram
• Basic vector operations
• Cross product
• Geometric interpretation

What are vectors?

A vector is a Latin word that means carrier. Vectors carry information from point A to point B. The length of the line between the two points A and B is called the magnitude of the vector, and the direction of the The displacement of point A from point B is called the direction of the vector AB. Vectors are also called Euclidean vectors or spatial vectors. Vectors have many applications in math, physics, computer science, engineering, and various other fields. [Refer Fig. 1]

                 Fig. 1: Vector a

Formula for the area of a parallelogram

The area of a parallelogram is the base times the height. The area of a parallelogram is A = b x h.

Parallelogram law of addition of vectors

The law states that if two co-initial vectors A and B act simultaneously, represented by the two adjacent sides AB & AD of a parallelogram ABCD, then the diagonal of the parallelogram AC represents the sum of the two vectors A and B. That is, the resultant vector starts from the same initial point. [Refer Fig. 2]

    Fig. 2: Parallelogram ABCD

Triangle law of addition of vectors

The law states that if two sides of a triangle AB & BC with P and Q as magnitudes represent the two vectors acting simultaneously on a body in the same order, then the third side AC with R as the magnitude of the triangle represents the resultant vector R = P + Q. [Refer Fig. 3]

                           Fig. 3: Triangle law