Examples of scalar in the following topics:
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- While adding a scalar to a vector is impossible because of their different dimensions in space, it is possible to multiply a vector by a scalar.
- A scalar, however, cannot be multiplied by a vector.
- To multiply a vector by a scalar, simply multiply the similar components, that is, the vector's magnitude by the scalar's magnitude.
- Multiplying vectors by scalars is very useful in physics.
- For example, the unit of meters per second used in velocity, which is a vector, is made up of two scalars, which are magnitudes: the scalar of length in meters and the scalar of time in seconds.
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- Multiplying a vector by a scalar is the same as multiplying its magnitude by a number.
- In addition to adding vectors, vectors can also be multiplied by constants known as scalars.
- Examples of scalars include an object's mass, height, or volume.
- When multiplying a vector by a scalar, the direction of the vector is unchanged and the magnitude is multiplied by the magnitude of the scalar .
- (iii) Increasing the mass (scalar) increases the force (vector).
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- Physical quantities can usually be placed into two categories, vectors and scalars.
- In contrast, scalars require only the magnitude.
- Scalars differ from vectors in that they do not have a direction.
- Scalars are used primarily to represent physical quantities for which a direction does not make sense.
- This video introduces the difference between scalars and vectors.
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- Given this information, is speed a scalar or a vector quantity?
- Speed is a scalar quantity.
- Distance is an example of a scalar quantity.
- Scalars are never represented by arrows.
- (A comparison of scalars vs. vectors is shown in . )
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- For scalars, the obvious answer is the absolute value.
- The absolute value of a scalar has the property that it is never negative and it is zero if and only if the scalar itself is zero.
- A norm is a function from the space of vectors onto the scalars, denoted by $\| \cdot \|$ satisfying the following properties for any two vectors $v$ and $u$ and any scalar $\alpha$ :
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- The definition of such a space actually requires two sets of objects: a set of vectors $V$ and a one of scalars $F$ .
- For our purposes the scalars will always be either the real numbers $\mathbf{R}$ or the complex numbers $\mathbf{C}$ .
- Addition and scalar multiplication are defined component-wise:
- This implies the uniqueness of the zero element and also that $\alpha \cdot 0 = 0$ for all scalars $\alpha$ .
- And the minus element is inherited from the scalars: $[-f](t) = -f(t)$ .
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- This differentiates them from scalars, which are mere numbers without a direction.
- Andersen explains the differences between scalar and vectors quantities.
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- Recall that the electric potential V is a scalar and has no direction, whereas the electric field E is a vector.
- This is consistent with the fact that V is closely associated with energy, a scalar, whereas E is closely associated with force, a vector.
- Summing voltages rather than summing the electric simplifies calculations significantly, since addition of potential scalar fields is much easier than addition of the electric vector fields.
- The electric potential at point L is the sum of voltages from each point charge (scalars).
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- We have essentially stumbled upon a few nice four-vectors, but there is a more systematic way of dealing with four-vectors, scalars and other quantities like the transformation matrix $\Lambda^\mu_{~\nu}$.
- Let's say there is a scalar field defined over all spacetime.
- The quantity on the left is clearly a scalar because it is the different in the value of a scalar field at two points.
- If we take $A^{\mu}$ to be the vector potential plus the scalar potential,
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- that transforms as a scalar where $n(x^\alpha)$ is the number density.
- One could use it as the source for a scalar theory of gravity, but it would violate the equivalence principle.