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Get some graph paper, draw two axes and bisect them with a 45 degree sloping line.

Next pick any point on that 45 degree sloping line and from that point draw a line parallel to the horizontal axis so that it intersects the vertical axis.

Do the same thing from the point drawing a line parallel with the vertical axis so that it intersects the horizontal axis.

These two lines represent represent the components of your vector and if you measure them they will be of equal length and thus of equal magnitude.

For ANY angle of slope (other than 45 degrees) the two vectors will not be of equal length.

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Q: Why will the horizontal and vertical components of a vector be equal in magnitude if the angle is 45 degrees?
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