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Vector

Formula

componentes

Magnitude or Length

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by: jackson

Distance between two points

Unit Vector

Scalar projection and Vector projection

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

What is vector?

Dot produce

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:

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