Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 12.6 : Vector Functions
7. Identify the graph of the vector function without sketching the graph.
\[\vec r\left( t \right) = \left\langle {2 - t,4 + 7t, - 1 - 3t} \right\rangle \] Show SolutionThere really isn’t a lot to do with this problem. The equation should look very familiar to you. We saw quite a few of these types of equations in the Equations of Lines and Equations of Planes sections.
From those sections we know that the graph of this equation is a line in \({\mathbb{R}^3}\) that goes through the point \(\left( {2,4, - 1} \right)\) and parallel to the vector \(\vec v = \left\langle { - 1,7, - 3} \right\rangle \).