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Byju's Answer
Standard XII
Mathematics
Equation of a Plane Passing through Three Points
Using directi...
Question
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.
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Solution
The
given
points
are
A
2
,
3
,
-
4
,
B
1
,
-
2
,
3
and
C
3
,
8
,
-
11
.
We
know
that
the
direction
ratios
of
the
line
joining
the
points
,
x
1
,
y
1
,
z
1
and
x
2
,
y
2
,
z
2
are
x
2
-
x
1
,
y
2
-
y
1
,
z
2
-
z
1
.
The
direction
ratios
of
the
line
joining
A
and
B
are
1
-
2
,
-
2
-
3
,
3
+
4
,
i
.
e
.
-
1
,
-
5
,
7
.
The
direction
ratios
of
the
line
joining
B
and
C
are
3
-
1
,
8
+
2
,
-
11
-
3
,
i
.
e
.
2
,
10
,
-
14
.
It
is
clear
that
the
direction
ratios
of
BC
are
-
2
times
that
of
AB
,
i
.
e
.
they
are
proportional
.
Therefore
,
AB
is
parallel
to
BC
.
Also
,
point
B
is
common
in
both
AB
and
BC
.
Therefore
,
points
A
,
B
and
C
are
collinear
.
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0
Similar questions
Q.
Show that the points
A
(
2
,
3
)
,
B
(
4
,
0
)
and
C
(
6
,
−
3
)
are collinear.
Q.
Show that the points
(
2
,
3
)
,
(
3
,
1
)
and
(
1
,
5
)
are collinear.
Q.
By using slopes, show that the following points are collinear
D
(
5
,
1
)
,
E
(
1
,
−
1
)
,
R
(
11
,
4
)
Q.
Prove that, the points (1,5),(2,3), and (-2,-11) are not collinear.
Q.
If the points
(
a
1
,
b
1
)
,
(
a
2
,
b
2
)
and
(
a
1
+
a
2
,
b
1
+
b
2
)
are collinear, then show that
a
1
b
2
=
a
2
b
1
.
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Equation of a Plane Passing through Three Points
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