Vector Multiplication
Vector Multiplication - Related Videos
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 20 •
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.
07:57
Direct Injection of a Lentiviral Vector Highlights Multiple Motor Pathways in the Rat Spinal Cord
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Cited by 4 •
2019
This protocol demonstrates injection of a retrogradely transportable viral vector into rat spinal cord tissue. The vector is taken up at the synapse and transported to the cell body of target neurons. This model is suitable for retrograde tracing of important spinal pathways or targeting cells for gene therapy applications.
11:35
The Multiple Sclerosis Performance Test (MSPT): An iPad-Based Disability Assessment Tool
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Cited by 104 •
2014
Precise measurement of neurological and neuropsychological impairment and disability in multiple sclerosis is challenging. We report methodologic details on a new test, the Multiple Sclerosis Performance Test (MSPT). This new approach to the objective of quantification of MS related disability provides a computer-based platform for precise, valid measurement of MS severity.
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
A scalar applies the same multiplication factor to every component of a vector. This changes the vector’s magnitude while treating its components consistently. In physics, that provides a controlled way to rescale displacement, velocity, or force without independently altering their component relationships. The resulting quantity remains a vector, so it can still be interpreted through magnitude and direction.
The dot product pairs corresponding components and combines them into one scalar. Because no vector direction remains in the result, it is suited to physical quantities represented by scalar outcomes. In mechanics, work is an important application: the operation connects force and displacement in a calculation whose result is not itself a direction.
Because the cross product’s magnitude depends on the lengths of the vectors and their included angle, changing the angle can change the result even when the vector lengths stay fixed. The operation also produces a perpendicular vector, so it carries directional information. This geometric behavior supports calculations involving torque, angular momentum, and magnetic effects.
Choose a dot product when the required output is a scalar, as in work. Choose a cross product when the required output is a perpendicular vector, as in torque, angular momentum, or magnetic effects. The distinction is therefore not merely algebraic: it determines whether the calculation produces a scalar result or a new vector with directional meaning.
First identify whether a scalar or another vector is being combined, then determine whether the physical quantity requires a vector or scalar output. For scalar multiplication, apply the same scalar to each component. For a dot product, combine corresponding components. For a cross product, track the perpendicular direction and the roles of vector lengths and included angle.
Vector multiplication connects vector quantities to different kinds of physical results. Scalar multiplication can rescale displacement, velocity, or force; dot-product reasoning supports work; and cross-product reasoning supports torque, angular momentum, and magnetic effects. These applications show why component calculations and geometric interpretation are both important in mechanics, electromagnetism, and other areas of physical science.