## Linear Algebra: A Modern Introduction

Vector form:$\begin{bmatrix}{x \\y \\z}\end{bmatrix} = t\begin{bmatrix}{1 \\-1\\4}\end{bmatrix}$ Parametric form: $x=t, y=-t,z=4t$
The vector form of a line is: $x=p+td$ This implies, $\begin{bmatrix}{x \\y \\z}\end{bmatrix} = \begin{bmatrix}{0 \\0 \\0}\end{bmatrix}+t\begin{bmatrix}{1 \\-1\\4}\end{bmatrix}$ or, $\begin{bmatrix}{x \\y \\z}\end{bmatrix} = t\begin{bmatrix}{1 \\-1\\4}\end{bmatrix}$ And Parametric equations of a line are defined as such equations which correspond to the components of the vector. Thus, the parametric form of the equation of a line is: $x=t, y=-t,z=4t$ Hence, the vector form is:$\begin{bmatrix}{x \\y \\z}\end{bmatrix} = t\begin{bmatrix}{1 \\-1\\4}\end{bmatrix}$ Parametric form: $x=t, y=-t,z=4t$