Vector Calculus Ch. 1 - Key Terms

component

a scalar that describes either the vertical or horizontal direction of a vector

coordinate plane

a plane containing two of the three coordinate axes in the three-dimensional coordinate system, named by the axes it contains: the xy-plane, xz-plane, or the yz-plane

cross product

cylinder

a set of lines parallel to a given line passing through a given curve

cylindrical coordinate system

a way to describe a location in space with an ordered triple (r,θ,z), where (r,θ) represents the polar coordinates of the point’s projection in the xy-plane, and z� represents the point’s projection onto the z-axis

determinant

a real number associated with a square matrix

direction angles

the angles formed by a nonzero vector and the coordinate axes

direction cosines

the cosines of the angles formed by a nonzero vector and the coordinate axes

direction vector

a vector parallel to a line that is used to describe the direction, or orientation, of the line in space

dot product

u⋅v=u1v1+u2v2+u3v3

ellipsoid

elliptic cone

elliptic paraboloid

general form of the equation of a plane

an equation in the form ax+by+cz+d=0, where n=⟨a,b,c⟩ is a normal vector of the plane, P=(x0,y0,z0) is a point on the plane, and d=−ax0−by0−cz0

hyperboloid of one sheet

hyperboloid of two sheets

normal vector

a vector perpendicular to a plane

normalization

using scalar multiplication to find a unit vector with a given direction

orthogonal vectors

vectors that form a right angle when placed in standard position

parallelogram method

a method for finding the sum of two vectors; position the vectors so they share the same initial point; the vectors then form two adjacent sides of a parallelogram; the sum of the vectors is the diagonal of that parallelogram