Question

Each vector12. Jacob has a vector j = < 4,8 > and he wants you to find the direction

Answer 1

The given vector is:

`\textbf{j}=\langle4,8\rangle`

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:

`\tan\theta=(y)/(x)`

Substitute y=8 and x=4 into the formula:

`\tan\theta=(8)/(4)=2\Rightarrow\theta=\arctg(2)\approx63.43^(\circ)`

The direction of the vector is about 63.43º counterclockwise from the east.