Question

The horizontal component of vector a is equal to the vertical component of vector b. If 30 degrees is the angle made by vector a with its vertical axis and that made by vector b with its horizontal Axis, then calculate the value of vector b in terms of vector a.

Answer 1

From the figure given above,

The horizontal component of a = $acos\left({30}^o\right)$

The vertical component of b = $bsin\left({30}^o\right)$

Now, by equating the equal components, we will get,

$acos\left({30}^o\right)=bsin\left({30}^o\right)$

$b=acot\left({30}^o\right)=\sqrt{3}a$.

Thus the vector b is $\sqrt{3}$ times the vector a.