The dot product is a scalar that is equal to the length of the projection of one vector X onto a unit vector pointing in the same direction as another vector Y, provided that X and Y start in the same location. The cross product is a vector that is perpendicular to two other vectors X and Y.
Continue ReadingThe dot product is calculated by multiplying together the first element, the second element and so on of X and Y; these products are summed to yield the dot product. The dot product is also found by multiplying together the length of X, the length of Y and the cosine of the angle between X and Y. Calculating the cross product requires finding the determinant of a matrix in which the first row contains unit vectors, the second row contains the vector X and the third row contains the vector Y. Although the dot product is commutative (X dot Y is the same quantity as Y dot X), the cross product is not. X cross Y is the determinant of the matrix described above, while Y cross X is the determinant of the matrix where the first row contains unit vectors, Y is the second row and X is the third row.
Learn more about CalculusA good application for vector analysis is the calculation of an airplane's flight path. This requires knowing the magnitude and direction of both the plane's thrust, as well as that of the prevailing winds acting on the plane.
Full Answer >The square root function in MATLAB is sqrt(a), where a is a numerical scalar, vector or array. The square root function returns the positive square root b of each element of the argument a, such that b x b = a.
Full Answer >"Cot" is the abbreviation for "cotangent," a trigonometric function used to find the value of an angle in a right triangle by dividing the length of an adjacent side by the length of the opposite side. The numerical value of cot x varies depending on the value of x.
Full Answer >There are many applications in which calculus is used in real life, such as calculating minimum payments due on credit cards, determining the length of cable required to connect two substations and evaluating survey data. Just as geometry is the mathematical study of shapes, calculus is the mathematical study of change.
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