As $t$ changes, what happens to the tip of the vector $\vec{r}=(1+4 t) \vec{i}+(2-3 t) \vec{j}$ ?
A) It moves in a straight line parallel to the vector $3 \vec{i}+1 \vec{j}$.
B) It moves in a straight line parallel to the vector $\vec{i}+2 \vec{j}$.
C) It moves in a straight line parallel to the vector $4 \vec{i}-3 \vec{j}$.
D) None of the above.

Question

Quizplus · Accepted Answer

The vector $\vec{r}=(1+4t)\vec{i}+(2-3t)\vec{j}$ has a direction vector of $4\vec{i}-3\vec{j}$, indicating it moves in a straight line parallel to this vector.

As ttt Changes, What Happens to the Tip of the Vector r⃗=(1+4t)i⃗+(2−3t)j⃗\vec{r}=(1+4 t) \vec{i}+(2-3 t) \vec{j}r=(1+4t)i+(2−3t)j​

As $t$ Changes, What Happens to the Tip of the Vector $\vec{r}=(1+4 t) \vec{i}+(2-3 t) \vec{j}$