Can a rectangular component of a vector be greater than the vector itself?
Think about it. The rectangular components are two adjacent sides of a rectangle whose diagonal is the vector. The diagonal of a rectangle is never less than the length of either of two adjacent sides. At the very most, one side can increase to approach the length of the diagonal, as the adjacent side decreases to approach zero. This happens when a vector of constant length rotates around the origin of an X-Y coordinate system. At zero, and at every integer multiple of pi radians thereafter, one of the rectangular components becomes zero when the other component is the length of the vector. Use a compass to draw a circle centered on the origin of an X-Y coordinate system. Then draw a vector from the origin to a length equal to the radius of the circle. Draw pairs of lines, parallel to the coordinate axes, from the point where the vector tip lies on the circle. Where each line-pair intersects an X-Y axis you can plot a point whose distance from the origin is the rectangular component of
