Therefore,
ˆ
ˆ
ˆ
xi
y j
z k
+
+
 =
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
5
2
4
( 3
2
8
)
i
j
k
i
j
k
+
−
+ λ
+
−
=
$
$
(5
3 )
(2
2 )
( 4
8 )
i
j
k
+ λ
+
+ λ
+ −
− λ
$
Eliminating λ , we get
5
3
x −
 =
2
4
2
8
y
z
−
+
=
−
which is the equation of the line in Cartesian form 11 3 2 Equation of a line passing through two given points
Let ar  and b
r
 be the position vectors of two
points A (x1, y1, z1) and B(x 2, y 2, z2),
respectively that are lying on a line (Fig 11