A quantity involving direction and magnitude is called physically vector A quantity involving direction and magnitude is called physically vector
Such a physical quantity is a vector.
a vector
a vector
Divergence is a vector operator that measures the magnitude of a vector fields source or sink at a given point.
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
Divergence is a measure of how a vector field spreads out or converges at a given point in space. It indicates whether the flow of a vector field is expanding or contracting at that point.
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
In the context of vector fields, divergence represents the rate at which the field's vectors are spreading out from or converging towards a point. It indicates how much the field is expanding or contracting at that point.
Free vectors have no fixed point of application and can be moved around without changing the physical meaning. Bound vectors are tied to a specific point and cannot be freely moved without altering the physical interpretation of the vector.
Such a physical quantity is a vector.
for a 3x3 matrix, it can be interpreted as the volume of the hexahedron formed by three vectors (each row of the matrix as one vector).
The same as the original vector. The scalar will change the numbers, but not the dimensions.
a vector
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a vector
For differentiation, you have to divide a vector by a scalar. Therefore, you should get a vector.
To determine the velocity vector from a given position in a physical system, you can calculate the derivative of the position vector with respect to time. This derivative gives you the velocity vector, which represents the speed and direction of motion at that specific point in the system.