Match the equation with the graph shown in red below.
A) $\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t ^ { 3 } \mathbf { k } \quad 0 \leq t \leq 1$
B) $\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 1$
C) $\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t ^ { 2 } \mathbf { k } , \quad 0 \leq t \leq 1$
D) $ \mathbf { r } ( t ) = \mathbf { i } + t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4$
E) $\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 1$

Question

Match the equation with the graph shown in red below.  
A) $\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t ^ { 3 } \mathbf { k } \quad 0 \leq t \leq 1$ 
B) $\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 1$ 
C) $\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t ^ { 2 } \mathbf { k } , \quad 0 \leq t \leq 1$ 
D) $ \mathbf { r } ( t ) = \mathbf { i } + t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4$ 
E) $\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 1$

Quizplus · Accepted Answer

The graph shown represents a parabolic curve that opens upward in the z-direction. The only equation that matches this graph is C, where the z-coordinate is given by $t^2$, which produces a parabolic curve in the z-direction when plotted along with x and y coordinates.

Match the Equation with the Graph Shown in Red Below r(t)=ti+t2j+t3k0≤t≤1\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t ^ { 3 } \mathbf { k } \quad 0 \leq t \leq 1r(t)=ti+t2j+t3k0≤t≤1

Match the Equation with the Graph Shown in Red Below $\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + t ^ { 3 } \mathbf { k } \quad 0 \leq t \leq 1$