cross product

Examples of cross product in the following topics:

• The Cross Product

  • The cross product of two vectors is a vector which is perpendicular to both of the original vectors.
  • The cross product is a binary operation of two three-dimensional vectors.
  • If the two original vectors are parallel to each other, the cross product will be zero.
  • The cross product is denoted as $a \times b = c$.
  • The cross product is different from the dot product because the answer is in vector form in the same number of dimensions as the original two vectors, where the dot product is given in the form of a single quantity in one dimension.

• Summation Notation

  • Some formulas involve the sum of cross products.
  • The cross products (XY) are shown in the third column.
  • The sum of the cross products is 3 + 4 + 21 = 28.

• The Dot Product

  • The dot product takes two vectors and returns a single value.
  • The dot product can only be taken from two vectors of the same dimension.
  • The dot product is the sum of the product of the corresponding parameters.
  • Geometrically, the dot product is the product of the magnitudes of two vectors and the cosine of the angle between them.
  • This is different from the cross product, which gives an answer in vector form.

• A Physical Aside: Einstein coefficients

  • Fermi's Golden Rule relates the cross-section for a process to a quantum mechanical matrix element and the phase space available for the products.
  • Because quantum mechanics for the most part is time reversible, the cross-section for the forward and reverse reactions are related.

• Cross-Channel Customer Experience

  • New technology provides retailers with many different ways to market products and interact with customers.
  • The cross channel customer experience has changed the way that business is conducted.
  • A solid cross-channel strategy is essential to support buyers no matter how or where they access product information or whether they shop on line or in store or both simultaneously.
  • To be effective, multi-channel marketing must be supported by good supply chain management systems, so that product information and prices of goods are consistent across the various customer channels.
  • It facilitates data mining and makes decisions relating to products (pricing, development), management (financial forecasting and customer profitability) and marketing (customer acquisition, cross-selling and up-selling) more efficient and effective.

• Typing and Cross-Matching for Transfusions

  • Due to the different antigen blood types, blood must be cross-matched during processing to avoid potential complications.
  • Several laboratory tests allow cross-matching of compatible blood between donor and recipient.
  • Patients should ideally receive their own blood or type-specific blood products to minimize the chance of a transfusion reaction.
  • Risks can be further reduced by cross-matching blood, but this process isn't always performed if time is short and the need for transfusion has not been anticipated.
  • Explain the purposes of typing and of cross-matching blood prior to transfusion

• Cross-Price Elasticity of Demand

  • The cross-price elasticity of demand shows the relationship between two goods or services.
  • Cross-Price Elasticity of Demand (EA,B) is calculated with the following formula:
  • If two products are complements, an increase in demand for one is accompanied by an increase in the quantity demanded of the other.
  • The value of the cross-price elasticity for complementary goods will thus be negative .
  • A positive cross-price elasticity value indicates that the two goods are substitutes.

• Mendel's Law of Independent Assortment

  • The independent assortment of genes can be illustrated by the dihybrid cross: a cross between two true-breeding parents that express different traits for two characteristics.
  • The sorting of alleles for texture and color are independent events, so we can apply the product rule.
  • Round/green and wrinkled/yellow offspring can also be calculated using the product rule as each of these genotypes includes one dominant and one recessive phenotype.
  • Note that this process is a diagrammatic version of the product rule.
  • The forked-line method can be used to analyze a trihybrid cross.

• Control of Muscle Tension

  • Muscle tension is influenced by the number of cross-bridges that can be formed.
  • In individual muscle fibers, the amount of tension produced depends primarily on the amount of cross-bridges formed, which is influenced by the cross-sectional area of the muscle fiber and the frequency of neural stimulation.
  • Cross-bridges can only form where thick and thin filaments overlap, allowing myosin to bind to actin.
  • If more cross-bridges are formed, more myosin will pull on actin and more tension will be produced.
  • The primary variable determining force production is the number of myofibers (long muscle cells) within the muscle that receive an action potential from the neuron that controls that fiber.

• Cross-Training and Job Sharing

  • Cross training involves workers being trained in tangent job functions, while job sharing involves two people working together on the same job.
  • Cross-training in business operations involves training employees to engage in quality control measures.
  • Studies have shown that net productivity increases when two people share the same 40-hour job.
  • Workers on an assembly line, who normally do a single task, benefit from cross-training to develop their skills and be able to work on a variety of areas.