Math Insight

Applet: Line parametrization

The blue point $\color{blue}{\vc{x}}$ sweeps out the line parameterized by $\color{blue}{\vc{x}} = \color{red}{\vc{a}} + t\color{green}{\vc{v}}$, where $\color{red}{\vc{a}}$ is the red point and $\color{green}{\vc{v}}$ is the green vector. Change the line by dragging the red or green points. Change the position of $\color{blue}{\vc{x}}$ along the line by dragging the orange dot that determines the value of $t$. Dragging elsewhere on the figure rotates the graph. You cannot move $\color{blue}{\vc{x}}$ directly with the mouse.

Notice that when $t=0$, then $\color{blue}{\vc{x}}=\color{red}{\vc{a}}$. And when $t=1$, $\color{blue}{\vc{x}}$ is on top of the endpoint of the vector $\color{green}{\vc{v}}$, which is at position $\color{red}{\vc{a}}+\color{green}{\vc{v}}$.

Applet file: line_parametrization.m

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