682] 
and similarly 
FORMULAE RELATING TO THE RIGHT LINE. 
289 
CB h ° ad ^ 
Also, putting for shortness 
n = 
a, 
b, c 
, il' = 
a , b, c 
a', 
V, <t 
a', b', c' 
f, 
9, h 
/', 9\ h' 
we have 
Af+B 9 + Ch = ^- ¥) a, Af + Bg' + Oh' - ^- ¥) O', 
and finally, the determinant which multiplies F is 
sciLp) i( 6c ' - b ' c ?+V“' - c '“) 2 + (“ 6 ' - «'W=rfi-P) (1 “ n = V(1 " n 
We have thus the value of F\ forming in the same way those of G and 
find 
F = (i _ 02)! K a ~ a ' e ) a + O' “ a Q) il'}, 
G = ~4>)I № - ve ) n + (b'~ be) il'j, 
B={(0 - CO) a + (tf- c6) O'}, 
, we 
which, with the foregoing equations for A, B, G, give the six coordinates of the line 
of shortest distance.