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Tardigrade
Question
Mathematics
The distance between (2, 1, 0) and 2x + y + 2z + 5 = 0 is
Q. The distance between
(
2
,
1
,
0
)
and
2
x
+
y
+
2
z
+
5
=
0
is
1755
127
KEAM
KEAM 2017
Three Dimensional Geometry
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A
10
0%
B
10/3
0%
C
10/9
50%
D
5
50%
E
1
50%
Solution:
The distance of a point
(
x
1
,
y
1
,
z
1
)
from the plane
a
x
+
b
y
+
cz
+
d
=
0
is given by
=
∣
∣
a
2
+
b
2
+
c
2
a
x
1
+
b
y
1
+
c
z
1
+
d
∣
∣
∴
Distance of the point
(
2
,
1
,
0
)
from the plane
2
x
+
y
+
2
z
+
5
=
0
is equal to
=
∣
∣
(
2
)
2
+
(
1
)
2
+
(
2
)
2
2
×
2
+
1
×
1
+
2
×
0
+
5
∣
∣
=
∣
∣
4
+
1
+
4
4
+
1
+
5
∣
∣
=
3
10