what is the difference between scalar and a vector?
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The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions: Scalars are quantities that are fully described by a magnitude (or numerical value) alone. Vectors are quantities that are fully described by both a magnitude and a direction.
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Distance is a scalar quantity, it is a number given in some units. Position is a vector quantity. It has a magnitude as well as a direction. The magnitude of a vector quantity is a number (with units) telling you how much of the quantity there is and the direction tells you which way it is pointing.
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Weight is a force which is a vector and has a magnitude and direction. Mass is a scalar. Weight and mass are related to one another, but they are not the same quantity.
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The Dot Product gives a scalar (ordinary number) answer, and is sometimes called the scalar product. But there is also the Cross Product which gives a vector as an answer, and is sometimes called the vector product.
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The main difference lies in what the output of the operation is. A vector product takes two input vectors in a space and returns an output vector in the same space. A scalar product takes two input vectors in a space and returns a scalar value, usually either in the real field or the complex field.
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area is NOT a vector. But it can be "represented" by one. If you are dealing with planar regions in three dimensions, then it can be convenient to represent the "area" as a vector whose length is the actual scalar area and whose direction is perpendicular to the plane.
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A vector space is a set with an addition law and a scalar multiplication law, where the scalars are elements of a field. Thus, a vector space over a field may not be itself a field (e.g. continuous functions on an interval); however, a field is always a vector space over itself.
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Speed is a scalar, and average velocity is a vector. Average velocity indicates direction and can be represented as a negative number when the displacement is in the negative direction. Average speed does not indicate direction and can only be positive or zero.
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Cross Product The Dot Product gives a scalar (ordinary number) answer, and is sometimes called the scalar product. But there is also the Cross Product which gives a vector as an answer, and is sometimes called the vector product.
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Vectors are the physical quantities that have magnitude, answering how much; as well as direction, answering where to. For example: implies displacement of towards . A unit vector is a type of vectors such that the magnitude of it is one unit. For example: implies unit displacement towards .
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Matrices and scalar multiplication A matrix is a rectangular arrangement of numbers into rows and columns. ... The term scalar multiplication refers to the product of a real number and a matrix. In scalar multiplication, each entry in the matrix is multiplied by the given scalar.
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A vector is a number, while a scalar has a direction associated with a number. 3. Distance and speed are examples of scalar quantities while displacement and velocity are examples of vectors.
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In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars. For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars.
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Thrust is a vector quantity. pressure is the thrust acting on a given area. But pressure is a scalar quantity .
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Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor.
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Work is a scalar because it is the "dot" product of 2 vectors, also called the scalar product. W can also be expressed in terms of the components of the force and displacement vectors. Work is a vector because you multiply a force (a vector) by distance (a vector).
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A few of the most important are that Vector Spaces are closed both under addition and scalar multiplication. ... Being closed under addition means that if we took any vectors x1 and x2 and added them together, their sum would also be in that vector space. ex.