Vector Orientation
Vector Orientation - Related Videos
01:30
Oriented Surfaces
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2026
A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...
12:09
Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations
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Cited by 14 •
2013
A methodology to estimate ventricular fiber orientations from in vivo images of patient heart geometries for personalized modeling is described. Validation of the methodology performed using normal and failing canine hearts demonstrate that that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.
01:13
Location and Orientation of the Heart
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2024
The human heart, despite its modest size and weight, is an organ of remarkable strength and endurance. Roughly the size of a fist, the heart weighs between 250 and 350 grams and is nestled within the mediastinum, the medial cavity of the thorax. It extends obliquely for about 12 to 14 cm, resting on the superior surface of the diaphragm. The heart is positioned anterior to the vertebral column and posterior to the sternum, with two-thirds of its mass lying to the left of the midsternal line.
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.
FAQs
Coordinate components express a vector along the axes of a chosen reference frame, while direction cosines specify its directional relationship to those axes. Together, they provide a numerical description that engineers can use to represent forces, velocities, fields, or geometric relationships. This representation supports calculations in structural analysis, fluid mechanics, robotics, and other engineering systems.
The dot product measures how strongly one vector points in the direction of another. A larger positive result indicates greater alignment, whereas a result of zero indicates perpendicular directions. Engineers can therefore use it to compare orientations, assess directional relationships, and determine how vector quantities relate when analyzing forces, motion, or fields within a reference frame.
A cross product establishes a direction perpendicular to the two vectors being combined and represents rotational effects associated with their relative orientation. This makes it useful when engineering analysis must account for perpendicular directions or rotation. Its role complements the dot product: one evaluates alignment, while the other identifies perpendicular orientation and rotational relationships.
Begin by selecting the relevant reference frame, then resolve the vector into coordinate components or apply direction cosines. If the frame differs from the one used for analysis, apply a coordinate transformation, such as a rotation matrix. Finally, use dot or cross products when alignment, perpendicularity, or rotational effects must be evaluated.
They become important when a vector is described in one reference frame but must be interpreted in another. Rotation matrices provide a systematic way to change the vector's coordinate representation while preserving its geometric relationship. This is especially relevant to robotics, control systems, computer graphics, and engineering analyses involving changing orientations or moving frames.
Misaligned components or an inappropriate reference frame can change the calculated direction and contribution of a force, velocity, field, or geometric quantity. As a result, predicted motion, loading, or system behavior may differ substantially from the intended model. Careful orientation analysis is therefore important in structural analysis, fluid mechanics, robotics, and control applications.