Unit-2: Chp-2: Vector
PHYSICXION: Vector algebra is a branch of mathematics that deals with vectors. Vectors are quantities that have both magnitude and direction.
Vector algebra is a branch of mathematics that deals with vectors. Vectors are quantities that have both magnitude and direction. Vector algebra is used to perform operations on vectors, such as addition, subtraction, multiplication, and division. It is a powerful tool that is used in many areas of science and engineering, such as physics, engineering, chemistry, and computer science.
A brief view of its history:
Gibbs developed vector algebra as a way to simplify the mathematical notation for physical quantities that have both magnitude and direction, such as forces, velocities, and accelerations. He published his work on vector algebra in his book, Vector Analysis, which was published in 1901.
Heaviside developed vector algebra independently of Gibbs, and he used it to develop a new mathematical notation for electromagnetism. He published his work on vector algebra in a series of papers in the 1890s.
The work of Gibbs and Heaviside on vector algebra was instrumental in the development of modern physics and engineering. Vector algebra is now used in many areas of science and mathematics, including physics, engineering, chemistry, and computer science.
Here are some of the contributions of Gibbs and Heaviside to vector algebra:
A brief view of its history:
Gibbs developed vector algebra as a way to simplify the mathematical notation for physical quantities that have both magnitude and direction, such as forces, velocities, and accelerations. He published his work on vector algebra in his book, Vector Analysis, which was published in 1901.
Heaviside developed vector algebra independently of Gibbs, and he used it to develop a new mathematical notation for electromagnetism. He published his work on vector algebra in a series of papers in the 1890s.
The work of Gibbs and Heaviside on vector algebra was instrumental in the development of modern physics and engineering. Vector algebra is now used in many areas of science and mathematics, including physics, engineering, chemistry, and computer science.
Here are some of the contributions of Gibbs and Heaviside to vector algebra:
- They developed a notation for vectors that is still used today.
- They defined the basic operations of vector algebra, such as addition, subtraction, multiplication, and division.
- They developed the dot product and cross product, which are two important operations in vector algebra.
- They used vector algebra to solve problems in physics and engineering.
Interesting Facts:
- The vector triple product identity can be used to prove that the volume of a parallelepiped is equal to the product of its base area and its height.
- The vector triple product can be used to find the moment of inertia of a rigid body, which is a measure of its resistance to rotation.
- The vector dot product can be used to find the work done by a force over a displacement.
- The vector cross product can be used to find the torque produced by a force about a point.
- The vector dot product is commutative, but the vector cross product is not. This means that, a⋅b=b⋅a, but a×b≠b×a.
- The vector triple product identity states that, (a×b)⋅c=a⋅(b×c). This identity can be used to simplify vector expressions.
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CLASS NOTES :
Here full Class Notes Pdfs are attached, which will help you to score well in the exam.
NOTE-1: Theory of Vector Algebra.
NOTE-2: Solved Numerical (Easy and moderate level descriptive problems)
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