Question

The angle a vector makes with the x-axis of a coordinate system must be what size in order to make one or more of its components negative?

Answer 1

The 1st quadrant (0-90 degrees) is the only quadrant where none of the components are negative, so that means that any angle larger than 90 degrees will result in one of the components being negative.

Answer 2

Angle must be greater than 90 to make one or more components of a vector negative.

Step-by-step explanation:

There are four ranges of angle given below:

(i) For 0 < θ < 90, both components are positive.

(ii) For 90 < θ < 180, x-component is negative while y-component is positive.

(iii) For 180 < θ < 270, both components are negative.

(iv) For 270 < θ < 360, x-component is positive while y-component is negative.

Hence, angle must be greater than 90 to make one or more components of a vector negative.