Calculus III - Vector Functions

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Section 12.6 : Vector Functions

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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 Solution

There 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 \(\vec v = \left\langle { - 1,7, - 3} \right\rangle \).