Vector Components
Vector Components - Related Videos
01:08
Vector Algebra: Method of Components
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2023
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components. In many applications, the magnitudes and directions of...
01:29
Vector Components in the Cartesian Coordinate System
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2025
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
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.
08:08
Major Components of the Light Microscope
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2008
The light microscope is a basic tool for the cell biologist, who should have a thorough understanding of how it works, how it should be aligned for different applications, and how it should be maintained as required to obtain maximum image-forming capacity and resolution. The components of the microscope are described in detail here.
FAQs
The angle determines how much of a vector lies along each chosen axis. In two dimensions, the component adjacent to the reference angle uses Vx = V cos θ, while the perpendicular component uses Vy = V sin θ. A component receives a positive or negative sign according to whether the vector points in the positive or negative direction of that axis.
A suitable coordinate system can align axes with the important directions in a problem, so the resulting components are easier to interpret and combine. In Cartesian work, perpendicular x, y, and optionally z axes separate the vector into independent directional contributions. This choice is useful in complex physical systems because it clarifies which direction each part represents.
When several vectors act together, their x-components are combined with one another, and their y-components are combined separately; a z set can be treated likewise in three dimensions. This component-by-component approach reveals reinforcement or cancellation along individual directions, making the net effect easier to interpret in force, velocity, displacement, or field problems.
To resolve a vector, identify its magnitude, the coordinate axes, and the angle used to describe its direction. Apply Vx = V cos θ and Vy = V sin θ for a two-dimensional case, then assign signs from the vector's direction relative to each axis. In three-dimensional work, include the z component when needed. This workflow produces values ready for component-by-component addition.
In an equilibrium problem, forces can be resolved along the chosen axes and their corresponding components compared or added separately. Opposing contributions may cancel in one direction while remaining unbalanced in another, so the analysis identifies which directional parts require attention. This approach is especially useful when several forces act at different angles and direct geometric addition becomes difficult.
For projectile motion, separating a vector into perpendicular components lets the analysis track directional behavior independently. A velocity or displacement can therefore be represented through its contributions along the selected axes, rather than treated as one angled quantity. This organization simplifies calculations and interpretation of how motion develops in different directions.
Rotational analysis and three-dimensional modeling benefit from selecting axes that match the system being studied. Components then identify how a vector contributes along each relevant direction, including a z-axis when two dimensions are insufficient. The same representation supports forces, velocities, displacements, and fields, allowing complex physical systems to be described with organized directional data.