Question

The component of a vector $\overrightarrow{r}$ along $x$-axis will have a maximum value if:

• A. $\overrightarrow{r}$ along +ve $x$-axis
• B. $\overrightarrow{r}$ along +ve $y$-axis
• C. $\overrightarrow{r}$ along -ve $y$-axis
• D. $\overrightarrow{r}$ makes an angle of ${45}^o$ with the $x$-axis

Answer 1

The correct option is A $\overrightarrow{r}$ along +ve $x$-axis

Component of vector $r$ in $x$ direction, $|r_x|=r\cos \theta$

where $\theta$ is the angle between $\overrightarrow{r}$ and $x$ axis

As $|r_x|$ is maximum, thus $r\cos \theta$ is maximum.

This is possible only when $\cos \theta =1$

$⟹$ $\theta =0^o$

Hence, $\overrightarrow{r}$ is along +ve x-axis.