- #1
karush
Gold Member
MHB
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see post 3
Last edited:
karush said:$\tiny{s6.802.12.5.5}$
$\textsf{
Find a vector equation and parametric equations for:}\\$
$\textsf{The line through the point $(1,0,6)$}\\$
$\textsf{and perpendicular to the plane
$x=-1+2t, y=6-3 t, z=3+9t$}$
$\textit{looking at some examples but? } $
karush said:$\textsf{sorry copied problem incorrectly it should read}\\$
$\textsf{Find a vector equation and parametric equations for the line.}\\$
$\textsf{through the point $(1,0.6)$ and perpendicular to the plane $x+3y+z=5$!.}$
$\textit{the book answer to this was}\\$
$r=(i+6k)+t(i+3j+k)\\$
$x=1+t, y=3t, z=6+t$
$\textit{but don't know how it was derived!}$
A vector equation is an equation that represents a relationship between two or more vectors. It typically includes variables, constants, and vector operations such as addition, subtraction, and scalar multiplication.
A scalar equation involves only scalar quantities (numbers) and does not involve vectors or vector operations. A vector equation, on the other hand, involves vectors and vector operations and can represent more complex relationships between these quantities.
Parametric equations are a set of equations that express the coordinates of a point in terms of one or more parameters. These equations allow for a more flexible and intuitive representation of curves and surfaces in space.
To find a vector equation from parametric equations, you can simply express the coordinates of the point as a vector with the parameter as the variable. For example, if the parametric equations are x = t, y = 2t, z = 3t, the vector equation would be r = ti + 2tj + 3tk.
Vector and parametric equations are useful in science because they allow for a more precise and geometric representation of physical phenomena. They are especially useful in fields such as physics, engineering, and computer graphics, where calculations involving vectors and curves are common.