1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
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.
Open in App
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
.
Suggest Corrections
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
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Equation of a Plane: Three Point Form and Intercept Form
MATHEMATICS
Watch in App
Explore more
Equation of a Plane Passing through Three Points
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app
