Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra2 Marks
Question
Write down a unit vector in $XY-$plane, making an angle of $30^\circ$ with the positive direction of $x-$axis.
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Answer
Let $\overrightarrow r = x\widehat i + y\widehat j $ be a unit vector in $XY$ plane,
making angle $30^\circ$ with positive $X$ axis ,
so we have the vector as $\overrightarrow r = \cos {30^\circ}\hat i + \sin {30^\circ}\hat j$
$x = \frac{{\sqrt 3 }}{2};y = \frac{1}{2},\left( {\because \left| {\overrightarrow r } \right| = 1} \right).$
$\therefore \overrightarrow r = \frac{{\sqrt 3 }}{2}\widehat i + \frac{1}{2}\widehat j$ is the required vector.
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