what is the difference between scalar projection and vector projection?
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The vector projection of a vector onto a given direction has a magnitude equal to the scalar projection. ... A scalar projection is the length of the vector projection. It is given by the dot product of a vector with a unit vector for that direction.
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Scalar potentials are generally observed under static field conditions where as vector potentials are observed under dynamic conditions. Thus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field.
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A vector is a list of numbers (can be in a row or column), A matrix is an array of numbers (one or more rows, one or more columns).
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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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Lesson Summary A vector is an ordered list of elements and differs from a scalar by having both magnitude and direction. They are normally written either vertically as column vectors or horizontally as row vectors.
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The main difference between vector and raster graphics is that raster graphics are composed of pixels, while vector graphics are composed of paths.
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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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The main difference between vector and raster graphics is that raster graphics are composed of pixels, while vector graphics are composed of paths. A raster graphic, such as a gif or jpeg, is an array of pixels of various colors, which together form an image.
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A resultant is a vector. ... It is a scalar, not a vector itself. If you imagine a vector graphically as an arrow then it's magnitude represents the length of the arrow. A vector also has a direction, which is not included in a magnitude.
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Scalar quantities have only magnitude; vector quantities have both magnitude and direction. ... It has only magnitude, no direction. Force, displacement, and acceleration all occur with a designated direction.
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A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. ... For specifying that the scalars are real or complex numbers, the terms real vector space and complex vector space are often used.
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Rather than a grid of pixels, a vector graphic consists of shapes, curves, lines, and text which together make a picture. While a bitmap image contains information about the color of each pixel, a vector graphic contains instructions about where to place each of the components.
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By square of a vector we mean Dot Product with itself. Since, the projection of a vector on to itself leaves its magnitude unchanged, the dot product of any vector with itself is the square of that vector's magnitude(only).
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Scalar. The simple reason is unlike velocity or other vector quantities, it doesn't have a direction, it has a fixed path. Like; age cannot decrease but only increase in the same way for each person.
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Thrust is the force acting normal to the surface so we require both direction and magnitude of force for complete description of the force . hence it is an vector quantity . whereas pressure requires only its magnitude for its complete description , hence pressure is an scalar quantity .
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Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction. Force, displacement, and acceleration all occur with a designated direction.
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Any three vectors in R2 are linearly dependent since any one of the three vectors can be expressed as a linear combination of the other two vectors. You can change the basis vectors and the vector u in the form above to see how the scalars s1 and s2 change in the diagram.