Ncert Exercises & Solutions

The component of a vector \(\vec{r}\) along the X-axis will have maximum value if:

1.	\(\vec{r}\) is along the positive Y-axis.
2.	\(\vec{r}\) is along the positive X-axis.
3.	\(\vec{r}\) makes an angle of \(45^\circ\) with the X-axis.
4.	\(\vec{r}\) is along the negative Y-axis.

Hint: \(\vec a =|a| \hat a\)

Step: Find the maximum value of the horizontal component of the vector.
Let the X-axis component of \(\vec{r}\) make an angle \(\theta \) with the positive X-axis.
Then, the
\(\Rightarrow {r}_{{x}}=|{r}| \cos \theta~~~...(1)\)
For the maximum value of \({r}_{{x}}, \) \(\cos \theta\) should be maximum. Thus,
\(\Rightarrow \cos \theta =1 ~~~[\theta=0^\circ]\)
Substituting the value in \((1),\) we get;
\(\Rightarrow {r}_{{x}}=|{r}| \)
Since , \(\theta=0^\circ,\vec{r}\) is along the positive X-axis.
Hence, option (2) is the correct answer.

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