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

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

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

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

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

A
$\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}$
B
$\frac{1}{2} \hat{i} + \frac{\sqrt{3}}{2} \hat{j}$
C
$\frac{\sqrt{3}}{2} \hat{i} - \frac{1}{2} \hat{j}$
D
$\frac{1}{2} \hat{i} - \frac{\sqrt{3}}{2} \hat{j}$

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Basic , Modulus and Algebra of vectors

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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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