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# Parametric Equation of a Plane Calculator

Parametric equation refers to the set of equations which defines the qualities as functions of one or more independent variables, called as parameters. For instance, three non-collinear points a, b and c in a plane, then the parametric form (x) every point x can be written as x = c +m (a-b) + n (c-b). The simple parametric equation of a plane calculator is used to calculate the parametric form of a plane based on the point coordinates and the real numbers.

## Calculate the Parametric Form of a Plane

Parametric equation refers to the set of equations which defines the qualities as functions of one or more independent variables, called as parameters. For instance, three non-collinear points a, b and c in a plane, then the parametric form (x) every point x can be written as x = c +m (a-b) + n (c-b). The simple parametric equation of a plane calculator is used to calculate the parametric form of a plane based on the point coordinates and the real numbers.

#### Formula:

x = x1 + (a1*s) + (a2*t) y = y1 + (b1*s) + (b2*t) z = z1 + (c1*s) + (c2*t) Where, x,y,z = Coordinates a1,b1,c1 = Vector a2,b2,c2 = Vector x1,y1,z1 = Points of Coordinates s,t = Real Number

### Example:

Find the parametric equation of a plane if (x1, y1, z1) is (1,2,3) and (a1, b1, c1) is (3,4,5) and (a2, b2, c2) is (3,2,1) and s, t values are 7 and 9.

#### Solution:

x = x1 + (a1*s) + (a2*t)
= 1 + (3 x 7) + (3 x 9)
= 49

y = y1 + (b1*s) + (b2*t)
= 2 + (4 x 7) + (2 x 9)
= 48

z = z1 + (c1*s) + (c2*t)
= 1 + (5 x 7) + (1 x 9)
= 47