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The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs.
1.1×10 9 J: Magnetic stored energy in the world's largest toroidal superconducting magnet for the ATLAS experiment at CERN, Geneva [131] 1.2×10 9 J: Inflight 100-ton Boeing 757-200 at 300 knots (154 m/s) 1.4×10 9 J: Theoretical minimum amount of energy required to melt a tonne of steel (380 kWh) [132] [133] 2×10 9 J
The positions x 1 and x 2 of two bodies can be expressed in terms of their relative separation r and the position of their center of mass R cm Main article: Two-body problem The central-force problem concerns an ideal situation (a "one-body problem") in which a single particle is attracted or repelled from an immovable point O , the center of ...
~ 9.65 × 10 4 C: Charge on one mole of electrons (Faraday constant) [13] 10 5: 1.8 × 10 5 C: Automotive battery charge. 50Ah = 1.8 × 10 5 C: 10 6: mega-(MC) 10.72 × 10 6 C: Charge needed to produce 1 kg of aluminium from bauxite in an electrolytic cell [14] 10 7: 10 8: 5.9 × 10 8 C: Charge in world's largest battery bank (36 MWh), assuming ...
For instance, the points A = (1, 0, 0) and B = (0, 1, 0) in space determine the bound vector pointing from the point x = 1 on the x-axis to the point y = 1 on the y-axis. In Cartesian coordinates, a free vector may be thought of in terms of a corresponding bound vector, in this sense, whose initial point has the coordinates of the origin O = (0 ...
Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other.
For the intrinsic order of magnitude of magnetic fields, see: Orders of magnitude (magnetic moment). Note: Traditionally, the magnetizing field, H, is measured in amperes per meter. Magnetic induction B (also known as magnetic flux density) has the SI unit tesla [T or Wb/m 2]. [1] One tesla is equal to 10 4 gauss.