Question

Write down a unit vector in plane,making an angle of \(30°\)with the positive direction of \(x-axis.\)

Answer 1

If \(\vec{r}\) is a unit vector in the \(XY-\)plane,then \(\vec{r}=cosθ\hat{i}+sinθ\hat{j}.\)
Here,θ is the angle made by the unit vector with the positive direction of the \(x-axis.\)
Therefore,for \(θ=30°:\)
\(\vec{r}=cos30^{\degree}\hat{i}+sin30^{\degree}\hat{j}={\frac{\sqrt{3}}{2}}\hat{i}+\frac{1}{2}\hat{j}\)
Hence,the required unit vector is \({\frac{\sqrt{3}}{2}}\hat{i}+\frac{1}{2}\hat{j}\).