Question

which equation describes the sum of the vectors plotted below?
a. $vec{r}=3hat{x}-hat{y}$
b. $vec{r}=3hat{x}-2hat{y}$
c. $vec{r}=3hat{x}+2hat{y}$
d. $vec{r}=2hat{x}+hat{y}$

Explanation:

Step1: Analyze x - component

Count the number of units the vector moves in the x - direction. The vector moves 3 units to the right. In vector notation, the x - component of the resultant vector $\vec{r}$ is $3\hat{x}$.

Step2: Analyze y - component

Count the number of units the vector moves in the y - direction. The vector moves 1 unit down. In vector notation, the y - component of the resultant vector $\vec{r}$ is $- 1\hat{y}$.

Step3: Write the vector equation

The resultant vector $\vec{r}$ is the sum of its x and y components, so $\vec{r}=3\hat{x}-\hat{y}$.

Answer:

A. $\vec{r}=3\hat{x}-\hat{y}$