Suppose the coordinates of points P₁, P₂ and P₃ are being measured. When a line perpendicular to the straight line between P₁ and P₂ is drawn from point P₃, the range (P₁ P) between P₁ and P can be measured.

The coordinates of P₁, P₂, P₃ and P are as follows:

According to the above figure, vectors a and b will be as follows:

Suppose the angle formed by straight lines P₁, P₂ and P₁, P₃ is theta. By orthogonalizing straight lines P₁, P₂ and P₁, P₃, the equation to calculate the measurement of range (P₁ P) between P₁ and P will be as follows: