Question

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

Answer 1

Hi,

Any unit vector in XY plane will be of form

$\vec{A}$= cosФ $\hat{i}$ + sinФ$\hat{j}$ , where Ф is the

angle made by the vector with positive x-axis,

Given Ф = 30°,

So, cosФ = cos 30° = √3/2

sinФ = sin 30° = 1/2

Hence, the unit vector would be

$\vec{A}$= √3/2 $\hat{i}$ + 1/2$\hat{j}$

Hope, it helps !