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Tardigrade
Question
Mathematics
The foot of the perpendicular drawn from the point (4,2,3) to the line joining the points (1,2,3) and (1,1,0) lies on the plane:
Q. The foot of the perpendicular drawn from the point (4,2,3) to the line joining the points (1,2,3) and (1,1,0) lies on the plane:
3037
217
JEE Main
JEE Main 2020
Three Dimensional Geometry
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A
x
+
2
y
−
z
=
1
18%
B
x
−
2
y
+
z
=
1
15%
C
x
−
y
−
2
z
=
1
2%
D
2
x
+
y
−
z
=
1
65%
Solution:
Equation of
A
B
=
r
=
(
i
^
+
j
^
)
+
λ
(
3
j
^
−
3
k
^
)
Let coordinates of
M
=
(
1
,
(
1
+
3
λ
)
,
−
3
λ
)
.
PM
=
−
3
i
^
+
(
3
λ
−
1
)
j
^
−
3
(
λ
+
1
)
k
^
A
B
=
3
j
^
−
3
k
^
∵
PM
⊥
A
B
⇒
PM
.
A
B
=
0
⇒
3
(
3
λ
−
1
)
+
9
(
λ
+
1
)
=
0
⇒
λ
=
−
3
1
∴
M
=
(
1
,
0
,
1
)
Clearly M lies on
2
x
+
y
−
z
=
1
