Vector Volume
Vector Volume - Related Videos
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 •
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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.
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,...
03:20
Large-Scale Production of High-Capacity Adenoviral Vectors
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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.
02:41
Constant Volume Calorimetry
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2020
Calorimeters are useful to determine the heat released or absorbed by a chemical reaction. Coffee cup calorimeters are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow (or enthalpy change) accompanying processes that occur in solution at constant pressure. A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to measure the energy produced by reactions that yield large amounts of heat and...
01:30
Vectors
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2025
Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
FAQs
The cross product first combines two vectors into a perpendicular direction, establishing the normal to their shared plane. Taking the dot product with the third vector measures how strongly that vector projects along this normal. Applying the absolute value converts that scalar triple product into the nonnegative geometric magnitude used for the three-dimensional extent.
When three vectors are coplanar, the cross-product-based normal is perpendicular to their plane, while the remaining vector lies within that plane and has no component along the normal. Consequently, the dot product vanishes, so the computed volume is zero. This provides a direct test for whether the vectors occupy a common plane.
Increasing any vector’s length generally increases the possible extent, but the result also depends on separation angles. The angle between the first pair controls the size of their cross product, while the third vector’s alignment with the resulting normal controls its dot product. Perpendicular and well-separated directions therefore produce larger values than nearly parallel arrangements.
To calculate Vector Volume, form the cross product of two selected vectors, then take the dot product of the third vector with that cross-product result. Finally, apply the absolute value. This sequence establishes the two-vector plane first, then measures the third vector’s projection relative to its normal, producing the scalar used in geometric comparisons.
In physics, the quantity is useful when a problem represents a three-dimensional region through vector relationships rather than explicit boundary descriptions. It can support coordinate geometry and spatial modeling by reducing three directional inputs to one scalar extent. That scalar offers a compact way to compare configurations with different lengths or separation angles.
The absolute value ensures that the reported result is a nonnegative scalar magnitude, matching the geometric interpretation of extent rather than preserving a signed intermediate value. This makes the quantity suitable for comparing three-dimensional regions in coordinate geometry or spatial models, where the focus is the size of the resulting parallelepiped.