Objective
To verify the distributive property of vector multiplication, cтГЧ x (aтГЧ + bтГЧ) = cтГЧ x aтГЧ + cтГЧ x bтГЧ.
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]
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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]
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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 magnitude of the triangle, represents the resultant vector R = P + Q. [Refer Fig. 3]
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