The line passes through the point
(
1
,
2
,
−
4
)
.
The required line is perpendicular to the lines :
x
−
8
3
=
y
+
19
−
16
=
z
−
10
7
and
x
−
15
3
=
y
−
29
8
=
z
−
5
−
5
Therefore, required line is parallel to :
∣
∣
∣
∣
∣
ˆ
i
ˆ
j
ˆ
k
3
−
16
7
3
8
−
5
∣
∣
∣
∣
∣
=
24
ˆ
i
+
36
ˆ
j
+
72
ˆ
k
Hence, required vector equation of line is :
→
r
=
ˆ
i
+
2
ˆ
j
−
4
ˆ
k
+
λ
(
24
ˆ
i
+
36
ˆ
j
+
72
ˆ
k
)
And, Cartesian equation is :
x
−
1
24
=
y
−
2
36
=
z
+
4
72
