Write down a unit vector in the XY-plane,maki | vedclass

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Question

(A) unit vector $\vec{r}$ in the $XY$-plane making an angle $	heta$ with the positive $x$-axis is given by $\vec{r} = \cos 	heta \hat{i} + \sin 	he

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}$

Vedclass · Answer

(A) unit vector $\vec{r}$ in the $XY$-plane making an angle $	heta$ with the positive $x$-axis is given by $\vec{r} = \cos 	heta \hat{i} + \sin 	heta \hat{j}$.Given $	heta = 30^{\circ}$.Substituting the value of $	heta$:$\vec{r} = \cos 30^{\circ} \hat{i} + \sin 30^{\circ} \hat{j}$Since $\cos 30^{\circ} = \frac{\sqrt{3}}{2}$ and $\sin 30^{\circ} = \frac{1}{2}$,we get:$\vec{r} = \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}$.

Write down a unit vector in the $XY$-plane,making an angle of $30^{\circ}$ with the positive direction of the $x$-axis.

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