Exercise · ZW-PARAMETRIC-CURVE-001 · ★☆☆ Basic
Let \(\mathbf r(t)=\langle 2t,\,t^2\rangle\). Which point corresponds to \(t=3\)?
Choose one option.
Show answer
- A. \((6,9)\)
Explanation
Substitute \(t=3\) into each component: \(x=2\cdot3=6\) and \(y=3^2=9\).
Review the concept: Parametric curve
A parametric curve is the path traced by a point in space when its coordinates depend on a parameter \(t\) through a vector-valued function \(\mathbf r\).
\[\mathbf r(t)=\langle x(t),y(t),z(t)\rangle,\quad a\le t\le b\]
More practice problems: parametric curve
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