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hallowon
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Homework Statement
Find a parametric equation of x-4y+2z-15 = 0
Homework Equations
The Attempt at a Solution
I know this is a plane in 3 space
the normal of this plane is (3,-4,2)
a point on this line is (15,0,0)
A scalar equation of a plane is a mathematical representation of a plane in three-dimensional space using only scalar quantities, such as constants and coefficients, instead of vector quantities.
A vector equation of a plane uses vector quantities, such as position vectors and direction vectors, while a scalar equation only uses scalar quantities. This makes the scalar equation simpler and easier to work with mathematically.
The variables in a scalar equation of a plane are typically represented as x, y, and z, which represent the coordinates of a point on the plane. The coefficients of these variables represent the slope or direction of the plane.
To convert a scalar equation of a plane into parametric form, you need to solve for one of the variables, typically z, in terms of the other two variables (x and y). Then, you can use this equation to express the coordinates of any point on the plane in terms of a parameter, often denoted by t or s.
The coefficients of x, y, and z in the scalar equation of a plane represent the components of the normal vector to the plane. This normal vector is perpendicular to the plane and can be used to determine the orientation and distance of the plane from the origin.