Questions: Match each graph with its equation.
vecr(t)=⟨cos(t), 2, sin(t)⟩
vecr(t)=⟨t, sin(t), 2⟩
vecr(t)=⟨cos(t), sin(t), t⟩
vecr(t)=⟨t, 2,(t-2)^2⟩
vecr(t)=⟨2, sin(t), cos(t)⟩
Transcript text: -- wamap.org/assess2/?cid=386328aid=2203120\#/skip/2
Review 2
Score: 1.6/4 Answered: 1/4
Question 2
Match each graph with its equation.
\[
\begin{array}{l}
\vec{r}(t)=\langle\cos (t), 2, \sin (t)\rangle \\
\vec{r}(t)=\langle t, \sin (t), 2\rangle \\
\vec{r}(t)=\langle\cos (t), \sin (t), t\rangle \\
\vec{r}(t)=\left\langle t, 2,(t-2)^{2}\right\rangle \\
\vec{r}(t)=\langle 2, \sin (t), \cos (t)\rangle
\end{array}
\]
a.
b.
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Solution
Solution Steps
Step 1: Analyze Graph A
The graph for 'a' appears to be a parabola in the y-z plane, which suggests that y and z coordinates are quadratic functions and the x coordinate is constant.
Step 2: Analyze Graph B
The graph for 'b' shows a sinusoidal curve in the x-z plane, with a constant y value, suggesting that x and z are trigonometric functions of t, and y is a constant.
Step 3: Analyze Graph C
Graph 'c' resembles a semi-circle in the x-y plane, suggesting x and y coordinates are trigonometric functions and z is linearly dependent on the parameter t.
Final Answer:
a. $\vec{r}(t) = \langle 1, 2, (t-2)^2 \rangle$
b. $\vec{r}(t) = \langle t, \sin(t), 2 \rangle$
c. $\vec{r}(t) = \langle \cos(t), 2\sin(t), t \rangle$