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componentes
Magnitude or Length
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Distance between two points
Unit Vector
The dot produce is defined as follow for algebraic vectors in R2 and R3
Thus, mathematically, the scalar projection of b onto a is |b|cos(theta) (where theta is the angle between a and b) which from (*) is given by
If vector a =(a1,a2) and vector b=(b1,b2), then a.b= a1b1+a2b2
If vector a=(a1,a2,a3) and vector b=(b1,b2,b3), then a.b=a1b1+a2b2+a3b3
This quantity is also called the component of b in the a direction (hence the notation comp). And, the vector projection is merely the unit vector a/|a| times the scalar projection of b onto a:
The length of vector
The dot product of two vectors a and b (sometimes called the inner product, or, since its result is a scalar, the scalar product) is denoted by a ∙ b and is defined as:
The length or magnitude or norm of the vector a is denoted by ‖a‖ or, less commonly, |a|, which is not to be confused with the absolute value (a scalar "norm").
The length of the vector a can be computed with the Euclidean norm:
Vector (English: vector, also known as vector) is a mathematical, physical and engineering science and other natural science in the basic concept, that has a size and direction (such as: East, South, West, North) geometric objects , Often known as an arrow symbol to distinguish it from other quantities.
where θ is the measure of the angle between a and b. Geometrically, this means that a and b are drawn with a common start point and then the length of a is multiplied with the length of the component of b that points in the same direction as a.
The dot product can also be defined as the sum of the products of the components of each vector as: