Solution The vector equation of the line through the points A and B is
 rr  =
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
3
4
[ (5
3)
(1
4)
(6
1)
]
i
j
k
i
j
k
+
+
+ λ
−
+
−
+
−
i e rr  =
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
3
4
( 2
3
5
)
i
j
k
i
j
k
+
+
+ λ
−
+ (1)
Let P be the point where the line AB crosses the XY-plane