Vector algebra is used to accomplish several algebraic operations involving vectors. The word vector is derived from the Latin word vector, which literally means “carrier.” Vectors are used to convey data from point A to point B. The length of the line connecting two places A and B is the magnitude of the vector, and the direction of the vector AB is the direction of displacement of point A to point B. Vectors are also known as Euclidean vectors and spatial vectors. Vector algebra is utilized widely in arithmetic, physics, engineering, and a variety of other topics.
In physics and engineering, applications of vector algebra are used to execute addition and multiplication operations on physical values represented as vectors in three-dimensional space. Let’s take a closer look at vector algebra, its operations, and its applications.
Operations in Vector Algebra
Without the need for a coordinate system, several basic vector algebra operations can be performed geometrically. Vectors can be used to perform operations such as addition, subtraction, and multiplication by a scalar. Other methods of multiplying vectors include the dot product and cross product of vectors. The many operations in vector algebra are listed below.
- Addition of Vectors
- Subtraction of Vectors
- Scalar Multiplication
- Scalar Triple Product of Vectors
- Multiplication of Vectors
Applications of Vector Algebra
The subject of vector algebra is quantities that have both a direction and a magnitude. Many quantities, including velocity, acceleration, and force, must be expressed mathematically and can be represented as vectors. The following are some applications of vector algebra.
- Vectors are particularly important in the study of electromagnetic fields, gravitational fields, and fluid flow in physics and engineering.
- The component of a force in a specific direction can be determined by vector algebra.
- Vector algebra is used in physics to determine the interaction of two or more quantities.
Applications of Vector Algebra in Daily Life
A Canon is a piece of artillery that uses gun power or any other explosives based on propellant to launch a projectile. Cannons vary in caliber, firepower and mobility.
In Sports like basketball, and baseball vectors are unconsciously used by players. Ultimately they shoot the target or throw the ball in the direction at an angle which is done by knowledge. The same phenomena could be observed in cricket as well for catching the ball and hitting the shot.
Vectors in Gaming are used to store positions, directions and velocities. The position vector indicates how far the velocity vector indicates how much time it will take and how much force we should give and the direction vector indicates in which way we should apply the force.
Designing Roller Coasters
When a train reaches its peak point and rides downhill it gains enough speed for gravitational pull. With its speed to climb the next hill. This procedure happens again and again until it loses its friction. The train will keep on running until the next peak is higher than the first peak.
A wind that has a perpendicular component to the line or direction of travel. When a plane comes to land sometimes it faces difficulties for crosswinds. A pilot can find out the resultant velocity and direction with the help of a vector.
Boat Crossing a River
When a boat crosses a river the two velocities work together- the velocity of the river and the velocity of the boat. The direction of the boat changes with respect to the velocity of the river. So, the boatman finds an angle for crossing the river and reaching the bank of the river straightly.