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Q1   Write down a unit vector in XY-plane, making an angle of 30 \degree with the positive direction of x-axis.

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As we know 

a unit vector in XY-Plane making an angle \theta with x-axis :

\vec r=cos\theta \hat i+sin\theta \hat j

Hence for \theta = 30^0

\vec r=cos(30^0) \hat i+sin(30^0) \hat j

\vec r=\frac{\sqrt{3}}{2} \hat i+\frac{1}{2} \hat j

Answer- the unit vector in XY-plane, making an angle of 30 \degree with the positive direction of x-axis is

\vec r=\frac{\sqrt{3}}{2} \hat i+\frac{1}{2} \hat j

Posted by

Pankaj Sanodiya

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