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? A) Less the 30 degrees B) between 30 and 60 degrees C) between 61 and 90 degrees D) greater then 90 degrees

Answer 1

Greater than 90 degrees.

Explanation:

Let a vector R make angle
`\theta` with the x-axis. Then, the component along the x-axis would be

`R cos\theta`

Component along y-axis would be

`R sin\theta`

For
`0<\theta<90` both the components will be positive and lie in the first quadrant. If angle of vector is more than 90 degrees, one of the components would be negative. For example, angle between 90 to 180 degrees, x-component would be negative while between 180-270 degrees, both the components would be negative.

Answer 2

D) greater than 90 degrees

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An angle greater than 90 degrees will put it in the second quadrant, where the x-component is negative.