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?

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

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.

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