Vector Dot Product Calculus

Vector calculus or vector graphicysis is a branch of mathematics concerned with differentiation and integration of vector fields primarily in 3-dimensional Euclidean graphice. The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus which includes vector calculus as well as partial differentiation and multiple integration.In Euclidean graphice a Euclidean vector is a geometric object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its graphicgth and its direction is the direction that the arrow points. The magnitude of a vector a is denoted by .The dot product of two Euclidean vectors a and b is defined by ()where is the angle between the vectors and is the norm.It follows immediately that if is perpendicular to .The dot product therefore has the geometric interpretation as the graphicgth of the projection of onto the unit vector when the two vectors are placed so that their tails coincide.. By writing

Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quangraphicies in three-dimensional graphice and the way in which these quangraphicies vary.The gradient is a fancy word for derivative or the rate of change of a function. Its a vector (a direction to move) that. Points in the direction of greatest increase of a function (intuition on why)Is zero at a local maximum or local minimum (because there is no single direction of increase)

Section 5-4 Cross Product. In this final section of this chapter we will look at the cross product of two vectors. We should note that the cross product requires both of Vector Triple Product. The vector triple product idengraphicy is also known as the BAC-CAB idengraphicy and can be written in the formwhere x y and z are the projections of A upon the coordinate axes. When two vectors A 1 and A 2 are represented as. then the use of laws (3) yields for their sum. Thus in a Cartesian frame the sum of A 1 and A 2 is the vector determined by (x 1 y 1 x 2 y 2 x 3 y 3).Also the dot product