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Vector systems are a branch of mathematics that is used to manipulate measurements that have a value as well as a direction. Common examples are velocity, acceleration, force, etc - measurements involving motion. However, some motion-related measurements are not vectors. Distance, speed are not.
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What vector in a system points in the same direction as the linear momentum vector?
The energy vector, cmV = cP. The energy vector is parallel to the Momentum vector.
What is a projection of a vector along an axis of a coordinate system called?
The projection of a vector along an axis of a coordinate system is called a "component" of the vector. For a given vector, its component along a specific axis is determined by taking the dot product of the vector with a unit vector in the direction of that axis. This process effectively measures how much of the vector aligns with that axis. Each axis in the coordinate system has its own corresponding component of the vector.
What is state vector?
A state vector is a mathematical representation of the state of a system in a given moment, often used in physics and engineering. It consolidates all relevant variables into a single vector, allowing for concise analysis and manipulation of the system's dynamics. In quantum mechanics, for instance, a state vector describes the probability amplitudes of a quantum system's possible states. Overall, it serves as a crucial tool for understanding and predicting the behavior of complex systems.
What is the maximun no of components into which a vector can be split?
There is no maximum. A vector can be defined for a hyperspace with any number of dimensions. Such a hyperspace can be described using an orthogonal system of axes and the vector can be split into its components along each one of these axes.
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
What are the projections of a vector along the axes of a coordinate system?
A tangent of the vector is the projection of a vector along the axes of a coordinate system.
The components of a vector will be the same no matter what coordinate system is used to express that vector?
Yes, that is correct. The components of a vector, which represent its magnitude and direction in a particular coordinate system, are independent of the choice of coordinate system used to express the vector. This property is a fundamental characteristic of vectors in mathematics and physics.
What vector in a system points in the same direction as the linear momentum vector?
The energy vector, cmV = cP. The energy vector is parallel to the Momentum vector.
What is a projection of a vector along an axis of a coordinate system called?
The projection of a vector along an axis of a coordinate system is called a "component" of the vector. For a given vector, its component along a specific axis is determined by taking the dot product of the vector with a unit vector in the direction of that axis. This process effectively measures how much of the vector aligns with that axis. Each axis in the coordinate system has its own corresponding component of the vector.
How can one determine the velocity vector from a given position in a physical system?
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.
What are the Cartesian coordinates of the vector represented by the keyword "r vector"?
The Cartesian coordinates of the vector represented by the keyword "r vector" are the x, y, and z components of the vector in a three-dimensional coordinate system.
What number is the length of a vector?
The length of a vector is a scalar quantity, typically denoted as a positive real number, that represents the magnitude or size of the vector. It is calculated using the vector's components in a coordinate system, often with the Pythagorean theorem.
Is momentum a scalar quality?
A vector quantity is one which transforms like the coordinates. In other words, if a coordinate system is transformed by an operator , any vector quantity in the old coordinate system can be transformed to its equivalent in the new system by the same operator. An example of a vector quantity is displacement (r). If displacement is a vector, the rate of change of displacement (dr/dt) or the velocity is also a vector. The mass of an object (M) is a scalar quantity. Multiplying a vector by a scalar yields a vector. So momentum, which is the mass multiplied by velocity, is also a vector. Momentum too transforms like the coordinates, much like any other vector. The definition of a vector as a quantity having "magnitude and direction" is simply wrong. For example, electric current has "magnitude and direction", but is a scalar and not a vector.
What is the direction of zero vector?
The zero vector has no direction because it has a magnitude of zero. It is represented by a point at the origin in a coordinate system, with no specific direction.
Distance Vector protocols use what algorithm?
Distance Vector protocols use the Bellmanâ??Ford algorithm. The ARPANET system relied on Distance Vector protocols as their main routing technique in the early 80s.
What does the length of a position vector represent?
The length represents the magnitude or distance from the origin.
How can you represent vector quantities by using graph?
Vector quantities can be represented graphically by using arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. The starting point of the arrow can be placed at the origin of the coordinate system.
