Find the magnitude of the vector and the angle theta, 0 less than or equal to theta less than 360, that the vector makes with the positive x-axis. W=-4i-4square root of 3j

Question

The answer is either

1)W=5, theta =60

2) W=8, theta=60

3) W=6, theta =240

4) W=4, theta = 300

5) W=8, theta =240

Answer 1

First, to find the magnitude of the vector, we take the root sum square of the components. In doing this, we get sqrt(16+16*3)=sqrt(64)=8. So the magnitude is W=8.

Next, to find the angle it makes with the positive x-axis, we take the tangent inverse of the y component divided by the x component. From this, we get arctan(-4sqrt3 / -4) = arctan(sqrt(3)) = 60. However, this is the angle that this vector makes with the negative x-axis (if we draw it out). After drawing out the vector, it is clear that the angle we are looking for is 180 + 60 = 240 degrees.