Unit Vectors
Unit Vectors - Related Videos
03:38
Measurement: Standard Units
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2020
Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement (a unit), and an indication of the uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the errors in the measurement results. The number in the measurement can be represented in different ways, including decimal form and scientific notation, which is...
03:02
Measurement: Derived Units
0 Views •
2020
The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. These are called the SI base units. Units of measurement derived from the mathematical combination of SI base units are called SI-derived units. For example, the ratio of the SI unit for distance (meter; m) and the SI unit for time (second; s) gives the SI-derived unit...
09:20
Vectors in Multiple Directions
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2023
Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA This experiment demonstrates how vectors add and subtract in multiple directions. The goal will be to analytically calculate the addition or subtraction of multiple vectors and then to experimentally confirm the calculations. A vector is an object with both magnitude and direction. The magnitude of a vector is simply denoted as the length,...
10:42
A Protocol for the Production of Integrase-deficient Lentiviral Vectors for CRISPR/Cas9-mediated Gene Knockout in Dividing Cells
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Cited by 21 •
2017
We describe the production strategy of integrase-deficient lentiviral vectors (IDLVs) as vehicles for delivering CRISPR/Cas9 to cells. With an ability to mediate quick and robust gene editing in cells, IDLVs present a safer and equally effective vector platform for gene delivery compared to integrase-competent vectors.
03:20
Large-Scale Production of High-Capacity Adenoviral Vectors
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2026
Source: Ehrke-Schulz, E., et al. Cloning and Large-Scale Production of High-Capacity Adenoviral Vectors Based on the Human Adenovirus Type 5. J. Vis. Exp. (2016)This video demonstrates the large-scale amplification of high-capacity adenoviral vectors in suspension-adapted human embryonic kidney cells expressing Cre recombinase for use in gene delivery applications requiring high-titer, helper-free vector preparations.
FAQs
To obtain a unit vector, first determine the magnitude of a nonzero vector and then divide the vector by that magnitude. The result retains the original direction while removing its original size. This normalization allows the direction to be reused with different scalar magnitudes, such as when reconstructing a physical vector by multiplying the unit vector by a desired size.
The Cartesian basis vectors i, j, and k identify the x, y, and z directions, respectively. They let a physical vector be separated into directional components within a chosen coordinate system. Combining these basis directions with scalar component values provides a structured way to represent displacement, velocity, force, and fields in two or three dimensions.
Unit vectors provide explicit directional factors when vectors are combined through dot and cross products. Their use helps distinguish the directions associated with vector components from the scalar sizes multiplying them. Consequently, calculations involving physical quantities such as forces or fields can preserve directional information instead of treating each vector only as a magnitude.
A unit vector is interpreted relative to the coordinate system in which its direction is specified. Changing the chosen axes changes how a physical vector is described through components, even though the represented physical direction remains tied to the same system of coordinates. This makes unit vectors useful for clarifying coordinate transformations and organizing three-dimensional motion.
Begin by identifying the relevant coordinate directions, then assign the physical quantity's components to those directions using the corresponding basis vectors. If only a direction is needed, normalize the nonzero vector by its magnitude. To recover a quantity with a specified size, multiply the directional unit vector by the appropriate scalar magnitude.
In equilibrium analysis, unit vectors organize forces according to their coordinate directions so that the directional contributions can be examined separately. Representing each force through components makes it possible to compare opposing effects within the chosen axes. This supports a clearer assessment of whether the combined directional contributions satisfy the conditions being analyzed.
Unit vectors allow electric or magnetic fields, as well as displacement and velocity, to be written in terms of identifiable coordinate directions and component sizes. This separates where a quantity points from how large it is. The representation is especially useful when motion or field behavior must be tracked across multiple spatial directions in three-dimensional analysis.