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The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. Geometric interpretation
Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...
The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector.
Triple product is a ternary operation on vectors. It may also mean: Jacobi triple product, an identity in number theory; Triple product rule, a calculus chain rule for three interdependent variables; Lawson criterion, the product in nuclear fusion; Triple product property, an abstract algebra identity satisfied in some groups
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Michael Stifel published the following method in 1544. [3] [4] Consider the sequence of mixed numbers,,,, … with = + +.To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ).
World leaders have offered their condolences following the death of former US President Jimmy Carter, who passed away Sunday at the age of 100.
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