This means that any vector in the "ABC" reference frame will continue to have the same magnitude when rotated into the "AYC' " reference frame. Next, the following tensor rotates the vector about the new "Y" axis in a counter-clockwise direction with respect to the "Y" axis (The angle was chosen so that the "C' " axis would be pointed towards the corner of the box.): or Notice that the distance from the center of the sphere to the midpoint of the edge of the box is but from the center of the sphere to the corner of the box is . That is where the 35.26° angle came from. The angle can be calculated using the dot product. Let formula_47 be the unit vector in the direction of "C' " and let formula_48 be a unit vector in the direction of the corner of the box at  formula_49. Because formula_50  where formula_21 is the angle between formula_52 and formula_53 we have  The norm of the "K"2 matrix is also 1, so it too does not change the magnitude of any vector pre-multiplied by the "K"2 matrix. At this point, the "Z" axis is now orthogonal to the plane in which any "ABC" vector without a common-mode component can be found. Any balanced "ABC" vector waveform (a vector without a common mode) will travel about this plane. This plane will be called the zero plane and is shown below by the hexagonal outline. The "X" and "Y" basis vectors are on the zero plane. Notice that the "X" axis is parallel to the projection of the "A" axis onto the zero plane. The "X" axis is slightly larger than the projection of the "A" axis onto the zero plane. It is larger by a factor of . The arbitrary vector did not change magnitude through this conversion from the "ABC" reference frame to the "XYZ" reference frame (i.e., the sphere did not change size). This is true for the power-invariant form of the Clarke transform. The following figure shows the common two-dimensional perspective of the "ABC" and "XYZ" reference frames. It might seem odd that though the magnitude of the vector did not change, the magnitude of its components did (i.e., the "X" and "Y" components are longer than the "A", "B", and "C" components).