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.

(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 $θ$ $θ$ with a positive x-axis component of r along the X-axis

$\begin{matrix} r_{x} = | r | cos θ (r_{x})_{maximum} = | r | (cos θ)_{maximum} = | r | cos σ = | r | (∵ cos θ is maximum of θ = 0^{\circ}) As θ = 0 ° \end{matrix}$ $\begin{array}{l} r_{x} = | r | \cos θ \\ (r_{x})_{maximum} = | r | (\cos θ)_{maximum} \\ = | r | \cos σ = | r | (∵ \cos θ is maximum of θ = 0^{\circ}) \\ As θ = 0 ° \end{array}$

r is along the positive x-axis.

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