Vector Triple Product
Vector Triple Product - Related Videos
01:06
Scalar and Vector Triple Products
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2023
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors. The scalar triple product is the dot product of a vector with the cross product of two 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.
01:17
Vector Product (Cross Product)
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2023
Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule. Consider the cross product of two vectors. Imagine rotating the first vector about...
01:17
Vector or Cross Product
0 Views •
2023
Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule. Consider the cross product of two vectors. Imagine rotating the first vector about...
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
Cross products cannot be treated as associative, so the parentheses in a × (b × c) are essential. Replacing this expression with (a × b) × c changes which pair is combined first and therefore changes the resulting vector. The stated identity provides a reliable way to preserve the intended order when simplifying nested cross products in physics.
The dot products a · c and a · b act as scalar weights for b and c, respectively. The identity therefore separates the nested operation into two scaled vectors and a subtraction: b(a · c) − c(a · b). This form makes the roles of projection-related quantities explicit and is often easier to evaluate than computing two cross products.
The planar result is not merely a geometric observation; it restricts the possible direction of the final vector. Since the expression is written as a combination of b and c, no separate direction outside their span is introduced by the nested operation. This provides a qualitative test for whether a calculated direction is algebraically and physically plausible.
First identify the nested order, such as a × (b × c), and then replace it with b(a · c) − c(a · b). Next evaluate the two dot products, multiply b and c by their respective scalar values, and subtract the resulting vectors. This procedure avoids carrying two successive cross-product operations through a longer derivation.
The relation helps simplify expressions in mechanics, electromagnetism, and geometry. In mechanics, it can clarify equations involving forces and torques; in electromagnetism, it can reduce nested vector expressions in field calculations; and in geometry, it exposes how directions and projections combine. Its usefulness comes from converting a nested operation into terms that are often easier to interpret.
A result obtained from a nested cross-product calculation can be compared with the expression b(a · c) − c(a · b). Agreement between the two forms supports the algebra and implementation, while a disagreement can signal an order, sign, or calculation error. The comparison also checks whether the final vector remains consistent with the span of b and c.