Adjusting formulas

I have attached an excel document. If I put in values from A1 to D1 such that SQRT(A1^2+B1^2+C1^2+D1^2)=1, and have A7=0 only some values, in which ABS(B7)+ABS(C7)+ABS(D7) does not equal 0, and only certain values for A1, B1, C1, and D1, will lead to D20=SQRT(2). Also if I reverse all the values of A1 through D1 or B7 through D7 it changes the absolute values for A19 through D19 instead of simply reversing all the values for A19 through D19. How can I adjust my formulas so that D20=SQRT(2) for any value of A1 through D1 in which SQRT(A1^2+B1^2+C1^2+D1^2)=1, and for any combination of B7 through D7, and in which ABS(B7)+ABS(C7)+ABS(D7) is not equal to 0, and whenever A7=0, without changing the formula in D20? Also how do I adjust the formulas so that reversing all the values for A1 through D1 or B7 through D7 reverses the values of A19 through D19 instead of changing the absolute values of A19 through D19? Also any change to the formulas needs to keep E19=1 without changing the formula in E19. Also A8 through D8 need to keep their formulas.

A1 through D1 contain the coordinates of a point on a 4d hypersphere with a radius of 1, and centered at the origin. A8 through D8 also contain the coordinates for another point on the same 4d hypersphere, which is a random point with a position vector perpendicular to the position vector of point (1,0,0,0). What I am trying to do is to mathematically rotate the 4d hypersphere so that the point (1,0,0,0) moves to the same coordinates specified by A8 through D8. I'm trying to calculate the coordinates that the point specified by A8 through D8 will end up at when I rotate the 4d hypersphere like this in A19 through D19.