Examples of vector area in the following topics:
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- Vectors require both a magnitude and a direction.
- The magnitude of a vector is a number for comparing one vector to another.
- In the geometric interpretation of a vector the vector is represented by an arrow.
- Some examples of these are: mass, height, length, volume, and area.
- An example of a vector.
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- In mathematical terms, the velocity of a fluid is the derivative of the position vector of the fluid with respect to time, and is therefore itself a vector quantity.
- The velocity vector has non-zero components in any orthogonal direction along which motion of the fluid occurs.
- Qualitatively, Figure 1 shows the notion of volumetric flow rate regarding a cross-sectional surface of area A.
- If the surface area in question is a flat, plane cross-section, the surface integral reduces as shown in Equation 2 , where A is the surface area of the surface in question and v is the flow velocity of the fluid.
- Thus, volumetric flow rate for a given fluid velocity and cross-sectional surface area increases as θ decreases, and is maximized when θ = 0.
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- All vectors have a length, called the magnitude, which represents some quality of interest so that the vector may be compared to another vector.
- Vectors, being arrows, also have a direction.
- To visualize the process of decomposing a vector into its components, begin by drawing the vector from the origin of a set of coordinates.
- This is the horizontal component of the vector.
- He also uses a demonstration to show the importance of vectors and vector addition.
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- Draw a new vector from the origin to the head of the last vector.
- Since vectors are graphical visualizations, addition and subtraction of vectors can be done graphically.
- This new line is the vector result of adding those vectors together.
- Then, to subtract a vector, proceed as if adding the opposite of that vector.
- Draw a new vector from the origin to the head of the last vector.
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- $(A - B)^2 = A^2 -2AB + B^2$: The areas of plane figures equal the sum of the areas of their parts.
- Logically a beginning knowledge of vectors, vectors spaces and vector algebra is needed to understand his ideas.
- Ladder Boom Rescue: Vector analysis is methodological.
- Every vector has a component and a magnitude-direction form.
- Newton used vectors and calculus because he needed that mathematics.
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- Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.
- 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.
- Most of the units used in vector quantities are intrinsically scalars multiplied by the vector.
- (i) Multiplying the vector $A$ by the scalar $a=0.5$ yields the vector $B$ which is half as long.
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- In addition to adding vectors, vectors can also be multiplied by constants known as scalars.
- 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 .
- Once you have the vector's components, multiply each of the components by the scalar to get the new components and thus the new vector.
- A useful concept in the study of vectors and geometry is the concept of a unit vector.
- A unit vector is a vector with a length or magnitude of one.
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- Another way of adding vectors is to add the components.
- If we were to add this to another vector of the same magnitude and direction, we would get a vector twice as long at the same angle.
- This new line is the resultant vector.
- Vector Addition Lesson 2 of 2: How to Add Vectors by Components
- This video gets viewers started with vector addition using a mathematical approach and shows vector addition by components.
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- Electric fields created by multiple charges interact as do any other type of vector field; their forces can be summed.
- More field lines per unit area perpendicular to the lines means a stronger field.
- As vector fields, electric fields exhibit properties typical of vectors and thus can be added to one another at any point of interest.
- Thus, given charges q1, q2 ,... qn, one can find their resultant force on a test charge at a certain point using vector addition: adding the component vectors in each direction and using the inverse tangent function to solve for the angle of the resultant relative to a given axis.
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- Given this information, is speed a scalar or a vector quantity?
- Displacement is an example of a vector quantity.
- In mathematics, physics, and engineering, a vector is a geometric object that has a magnitude (or length) and direction and can be added to other vectors according to vector algebra.
- (A comparison of scalars vs. vectors is shown in . )
- He also uses a demonstration to show the importance of vectors and vector addition.