Vector Products Definitions of Terms Vector Components: Given a vector, a, with its initial point at (x_{i} , y_{i} , z_{i}) and terminal point at (x_{t} , y_{t} , z_{t}) , the components are :
x_{a} =
x_{t} x_{i}
Unit Vectors: The components of a vector are multiplied by unit vectors, assigning directions to the components with respect to the x, y and z axes. The unit vectors are defined as :
i = (1, 0, 0)
Magnitude: a = The square root of x_{a}^{2} + y_{a}^{2} + z_{a}^{2} Angle: (a,b) means the angle between the vectors a and b
Cross Product: Defined as a third vector, c = a b sin (a,b)
Dot Product: Also called the scalar product,
defined by the formula a·b = a b cos (a,b).
The angle (a,b) is the smallest angle measured between the common initial point of the vectors.
Shortcuts
The Dot Product of perpendicular vectors is ZERO
Standard Angle Calculations
LINEAR ALGEBRA
The worksheet Working Point Coordinates, listed under
ANGLE CALCULATORS Custom Calculations
Vector products may be applied to problems involving
COMPOUND JOINERY For the purpose of calculating angles on the surfaces of planes, the length of a vector is irrelevant, only the direction is important. For example, a vector lying on the xaxis may be replaced by any vector (x, 0, 0). Vectors used to determine a cross product may possess any length and/or orientation, provided the vectors lie on the plane of interest. Furthermore, since there are actually two pairs of supplementary dihedral angles created by the intercept of two planes, cross products may be taken as a X b or b X a without affecting the resulting values of the dihedral angles.
Vector Products Calculator
