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Divergence: Vector Operator

Divergence: Vector Operator

Subject: Physics

Divergence The divergence is an operator, which takes in the vector-valued function defining this vector field, and outputs a scalar-valued function measuring the change in density of the fluid at each point. Let in three-dimensional…

Curl: Vector Operator

Curl: Vector Operator

Subject: Physics

In vector calculus, the curl is a vector operator that describes the insignificant rotation of a 3-dimensional vector field. If the vector field represents the flow velocity of a moving fluid, then the curl is…

Uses of Vector Operators

Uses of Vector Operators

Subject: Physics

Uses of vector Operators As Gradient Before defining and explaining gradient we need to know about differential operator (∆→) and scalar and vector field. Vector differential operator ∆: Sir Hamilton first introduced the vector differential…

Physical Significance of Gradient

Physical Significance of Gradient

Subject: Physics

Gradient tells you how much something changes as you move from one point to another (such as the pressure in a stream). The gradient is the multidimensional rate of change of a particular function. The…

Integration in Vector

Integration in Vector

Subject: Physics

Integration Suppose, a body is moving in a particular direction, i.e., it is moving along a straight line. Although the direction of velocity is fixed, its magnitude is varying. Let the magnitude of velocity v…

Differentiation of a Vector

Differentiation of a Vector

Subject: Physics

Differentiation of a Vector Let V→ (u) be a vector that depends on unit scalar operator u. In mathematical language V is a function of u. Then we can write, ∆R→/∆u = [∆R(u+∆u) – R…

General Rule for Differentiation of a Scalar Quantity

General Rule for Differentiation of a Scalar Quantity

Subject: Physics

General rule for differentiation of a scalar quantity is as follows: A scalar quantity is a one dimensional measurement of a quantity, like a temperature, or weight. It changes with the change in their magnitude.…

Vector Operator

Vector Operator

Subject: Physics

Operator is an English term. It is a mathematical symbol or index. It has no value of its own. For example: square, cube, root, sine, log, etc. But when they act on or be associated…

Cross Product of Unit Vectors

Cross Product of Unit Vectors

Subject: Physics

Cross product of unit vectors Let î, ĵ and ƙ be the unit vectors along the three co-ordinate axes X, Y and Z respectively which are perpendicular to each other [Figure]. Now, the cross or…

Determination of Work by Variable Force using Integral Calculus

Determination of Work by Variable Force using Integral Calculus

Subject: Physics

Determination of work by variable force using integral calculus: Suppose, a variable force is acting along x-axis on a body. Magnitude of the force depends on distance travelled by the body i.e., F is the…

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