Then
zk
jy
ix
r
ˆ
ˆ
ˆ
+
+
r=
; 
k
z
j
y
xi
a
ˆ
ˆ
ˆ
1
1
1
+
+
=
r
and
ˆ
ˆ
ˆ
b
a i
b j
c k
=
+
+
r
Substituting these values in (1) and equating the coefficients of ˆ
ˆ
,i
j  and kˆ , we get
x = x1 + λa;  y = y1 + λ b;  z = z1+ λc (2)
Fig 11 4
© NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
469
These are parametric equations of the line Eliminating the parameter λ from (2),
we get
1
x – x
a
 =
1
1
y – y
=z – z
b
c