### Vector

Transcript: 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: by: jackson THANK YOU Dot produce Magnitude or Length The dot produce is defined as follow for algebraic vectors in R2 and R3 Unit Vector Scalar projection and Vector projection The length of vector Formula Vector 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: componentes If vector a =(a1，a2) and vector b=(b1，b2), then a.b= a1b1+a2b2 What is vector? 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: 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. 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: Distance between two points 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 THANK YOU FOR WARTH If vector a=(a1,a2,a3) and vector b=(b1,b2,b3), then a.b=a1b1+a2b2+a3b3