When a rectangle is constructed in order to add velocities, what represents the resultant of the velocities?

Answer 1

A diagonal vector from origin to the opposite corner of the rectangle.

Answer 2

It is the diagonal, as the other answers indicate. But, because you constructed a "rectangle", we can call that diagonal a hypotenuse and invoke the Pythagorean Theorem.

So if the magnitudes of the two velocities are |A| and |B|, we can find the magnitude of the "resultant" |C| from |C|^2 = |A|^2 + |B|^2. And the angle of C, the vector, would be theta = arctan(|A|/|B|) if A is the Y direction velocity vector and B is the X. Thus, C = |C| in the theta direction.

You can check the sanity of your quantitative answers by drawing a so-called vector diagram. When adding two vectors, we put the tail of one to the head (pointing end) of the other. Makes no difference which head and which tail, the resultant will still be the same. Make sure the length of your two vectors reflects the magnitude of each, and the orientation of each vector reflects the direction.

Then to check your resultant, draw a third arrow starting with the exposed tail of one of added vectors and ending with the pointy end of the other added vector. The length of that third arrow is the magnitude of your resultant, and the orientation of that resultant is its direction. The sum of two vectors is always a vector.

Answer 3

The diagonal