parametric vector form
whenever a solution set is described explicitly with vectors (EX: x2[2 3 1] + x3[1 2 3]), we say that the solution is in …
The parametric vector form is a way to represent a vector equation for a line or a curve in three-dimensional space. It is also called the parameterization of the equation.
The parametric vector form typically expresses the position of a point on a line or a curve in terms of a parameter or a variable. This parameter is usually denoted by ‘t’ and can represent time or some other quantity.
For example, the parametric vector form of a line can be expressed as:
r = a + tb
where ‘r’ is the position vector of any point on the line, ‘a’ is a fixed point on the line, ‘b’ is the direction vector of the line, and ‘t’ is a parameter that varies along the line.
Similarly, the parametric vector form of a curve can be expressed as:
r = f(t)
where ‘r’ is the position vector of any point on the curve, ‘f(t)’ is a vector function that calculates the position of the point based on the value of the parameter ‘t’.
The parametric vector form is useful in many applications, such as computer graphics, physics, and engineering. It allows us to represent complex curves and surfaces with a simple equation, making them easier to visualize and manipulate.
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