Cross Product
Cross Product - Related Videos
01:25
Cross Product
0 Views •
2023
The cross product is a fundamental concept in vector algebra that is a vector operation on two different vectors to obtain a third vector. Unlike the scalar product, the cross product results in a vector quantity perpendicular to both the original vectors. The magnitude of the cross product is obtained by multiplying the magnitude of both the vectors and the sine of the angle between them. This means that a larger angle between the vectors will lead to a greater magnitude of the cross product.
01:17
Vector Product (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...
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...
01:27
Cross Product and Its Geometry
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2026
In three-dimensional space, any two non-zero vectors that are not parallel define a unique plane and geometrically outline a parallelogram. The cross product of these vectors results in a third vector that is orthogonal to the plane formed by the initial two. This vector not only encodes information about direction but also reflects important physical quantities in applied contexts.The orientation of the cross product vector is determined using the Right-Hand Rule. When the fingers of the right...
13:39
Protocol for Production of a Genetic Cross of the Rodent Malaria Parasites
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Cited by 9 •
2011
Genetic crosses of rodent malaria parasites are performed by feeding two genetically distinct parasites to mosquitoes. Recombinant progeny are cloned from mouse blood after allowing mosquitoes to bite infected mice. This video shows how to produce genetic crosses of Plasmodium yoelii and is applicable to other rodent malaria parasites.
FAQs
The angle between the input vectors controls the size of a cross-product result. Because the magnitude uses the sine of that angle, parallel or antiparallel vectors produce zero, whereas perpendicular vectors produce the largest value for fixed input magnitudes. This dependence helps physicists identify when an interaction has a maximal rotational or area-related effect.
The right-hand rule determines the direction: orient the fingers from the first vector toward the second, and the extended thumb indicates the result. This direction is perpendicular to both input vectors, so it identifies an axis rather than lying within their plane. That geometric information is important when describing rotation, torque, and angular momentum.
The determinant method organizes the unit-vector directions and the components of both input vectors into a compact array. Evaluating it produces the three components of the perpendicular result, including their signs. This approach is especially useful in physics because it converts the geometric operation into a systematic component calculation for quantities such as torque and angular momentum.
Torque is calculated by crossing the lever-arm vector with the applied force vector. The lever arm specifies the position relative to the rotation point, while the force contributes according to its orientation and size. The resulting vector gives the torque’s rotational axis and magnitude, allowing mechanics problems to connect force placement with rotational effects.
Angular momentum uses the position vector crossed with linear momentum to combine an object’s location and motion into a rotational quantity. The position determines the geometric relation to the reference point, while linear momentum supplies the motion term. The resulting vector describes rotational motion in a form suited to mechanics and orientation analysis.
For area calculations, combining two vectors with a cross product captures the area’s oriented character, including both size and perpendicular direction. The same operation also supports calculations involving electromagnetic forces, where vector orientation matters alongside magnitude. These uses show why the method extends beyond mechanics to geometric and field-related physics problems.