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.

(b) Hint: The value of cosine decreases with an increase in the angle.

Step 1: Find the horizontal component of the vector.

Let r makes an angle θ with a positive x-axis component of r along the X-axis

rx=|r|cosθ(rx) maximum =|r|(cosθ)  maximum =|r|cosσ=|r|                                     (∵ cosθ is maximum of θ=0 ) As    θ=0°

r is along the positive x-axis.