The given vector is:
[tex]\textbf{j}=\langle4,8\rangle[/tex]It is required to find the direction of the given vector.
Recall that the direction θ of a vector is the angle it forms with the horizontal, or, in the coordinate plane, with the positive x-axis.
For a vector given in component form j = , the direction is calculated using the tangent ratio:
[tex]\tan\theta=\frac{y}{x}[/tex]Substitute y=8 and x=4 into the formula:
[tex]\tan\theta=\frac{8}{4}=2\Rightarrow\theta=\arctg(2)\approx63.43^{\circ}[/tex]The direction of the vector is about 63.43º counterclockwise from the east.
