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Recent questions and answers in 3-D Geometry
Questions
>>
JEEMAIN and NEET
>>
Mathematics
>>
Class11
>>
3-D Geometry
If
O
is origin,
|
→
O
P
|
=
3
with
d
.
r
.
=
(
−
1
,
2
,
−
2
)
then the coordinate of
P
is ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q57
answered
Nov 7, 2017
by
priyanka.c
2
answers
If
A
,
B
,
C
are three points on
x
a
x
i
s
,
y
a
x
i
s
a
n
d
z
a
x
i
s
respectively which are at the distances
a
,
b
,
c
from origin respectively and
P
is a point which is equidistant from
A
,
B
,
C
,
O
then the coordinates of
P
is?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q99
answered
Jan 23, 2014
by
rvidyagovindarajan_1
1
answer
If
A
(
4
,
7
,
8
)
,
B
(
2
,
3
,
4
)
,
C
(
2
,
5
,
7
)
are vertices of a triangle then the length of internal bisector of angle
A
is ?
jeemain
math
class11
ch12
3d-geometry
easy
distance-between-two-points
q98
mock
answered
Jan 12, 2014
by
rvidyagovindarajan_1
1
answer
Find the angle between any two diagonals of a cube.
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q97
answered
Jan 12, 2014
by
rvidyagovindarajan_1
1
answer
The cosine of angle between the medians drawn from vertices of isosceles rt. angled triangle is?
jeemain
math
class12
ch12
3d-geometry
direction cosines
easy
q96
answered
Jan 12, 2014
by
rvidyagovindarajan_1
1
answer
If from a point
P
(
a
,
b
,
c
)
perpendiculars
P
A
,
P
B
,
are drawn on
y
z
a
n
d
z
x
planes. then the equation of the plane
O
A
B
is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q95
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
If the vertices of a triangle are
A
(
1
,
4
,
2
)
,
B
(
−
2
,
1
,
2
)
C
(
2
,
−
3
,
4
)
then the angle
B
= ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q94
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
The projection of a line segment on
x
,
y
,
z
axes are
12
,
4
,
3
respectively, then the length of the line segment is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q93
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
The locus of a point
(
x
,
y
,
z
)
for which
z
=
k
is a ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q92
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
The points
(
5
,
0
,
2
)
,
(
2
,
−
6
,
0
)
,
(
4
,
−
9
,
6
)
a
n
d
(
7
,
−
3
,
8
)
represent vertices of a ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q91
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
A line segment of length
21
has
d
.
r
.
=
(
2
,
−
3
,
6
)
and makes obtuse angle with
x
a
x
i
s
, then the components of the line segment (vector) are?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q90
answered
Jan 10, 2014
by
rvidyagovindarajan_1
1
answer
If
P
(
2
,
3
,
4
)
a
n
d
Q
(
1
,
b
,
1
)
are two points and
O
is origin such that
O
P
is
⊥
to
O
Q
, then
b
=
?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q89
answered
Jan 10, 2014
by
rvidyagovindarajan_1
1
answer
The point which divides the line joining the points
(
2
,
4
,
5
)
a
n
d
(
3
,
5
,
−
4
)
in the ratio
2
:
3
externaly lies on the plane?
jeemain
math
class11
ch12
3d-geometry
section formula
easy
q88
answered
Jan 10, 2014
by
rvidyagovindarajan_1
1
answer
If the plane
x
−
2
y
+
3
z
=
0
is rotated through a right angle about its line of intersection with the plane
2
x
+
3
y
−
4
z
−
5
=
0
, then the eqn. of the plane in its new position is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q87
answered
Jan 10, 2014
by
rvidyagovindarajan_1
1
answer
The angle between the lines
x
=
1
,
y
=
2
and
y
=
−
1
,
z
=
0
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q86
answered
Jan 9, 2014
by
rvidyagovindarajan_1
1
answer
The angle between the line formed by
3
x
−
7
y
−
5
z
=
1
and
8
x
−
11
y
+
2
z
=
0
and the line formed by
5
x
−
13
y
+
3
z
+
2
=
0
and
8
x
−
11
y
+
2
z
=
0
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q85
answered
Jan 9, 2014
by
rvidyagovindarajan_1
1
answer
The equation of projection of the line
x
−
1
2
=
y
−
2
1
=
z
−
3
3
on the plane
x
+
y
+
z
=
1
is given by ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
difficult
q83
answered
Jan 9, 2014
by
rvidyagovindarajan_1
1
answer
Equation of the line through the point
(
2
,
−
1
,
−
1
)
, which is parallel to the plane
4
x
+
y
+
z
+
2
=
0
ans is
⊥
to the line
x
=
y
−
2
=
z
−
5
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q84
answered
Jan 8, 2014
by
rvidyagovindarajan_1
1
answer
The direction cosine of a line which is
⊥
to two perpendicular lines whose direction cosines are
(
l
1
,
m
1
,
n
1
)
a
n
d
(
l
2
,
m
2
,
n
2
)
is ?
jeemain
math
class12
ch11
3d-geometry
direction cosines
easy
q82
answered
Jan 8, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane that meets the coordinate axes at the points
A
,
B
,
C
respectively and the centroid of the
Δ
A
B
C
is
(
2
,
1
,
5
)
is ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q81
answered
Jan 7, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane which makes double the intercepts of the plane
3
x
+
6
y
−
z
+
12
=
0
is ?
jeemain
math
class12
3d-geometry
easy
equations-of-planes
q80
ch11
answered
Jan 7, 2014
by
rvidyagovindarajan_1
1
answer
A line makes angle
θ
with both
x
a
x
i
s
and
z
a
x
i
s
. If it makes angle
α
with
y
a
x
i
s
and
sin
2
α
=
2
sin
2
θ
then
cot
2
θ
=
?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
medium
q79
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
A tetrahedron has vertices
O
(
0
,
0
,
0
)
,
A
(
1
,
2
,
1
)
B
(
2
,
1
,
3
)
C
(
−
1
,
1
,
2
)
. The angle between the faces
O
A
B
and
A
B
C
is ?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q78
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
The value of
k
for which the line
→
r
=
(
4
ˆ
i
+
2
ˆ
j
−
ˆ
k
)
+
λ
(
ˆ
i
−
k
ˆ
j
+
2
ˆ
k
)
lies on the plane
2
x
−
4
y
+
z
=
3
is ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q77
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
The value of
k
for which the line
x
−
4
1
=
y
−
2
1
=
z
−
k
2
to lie on the plane
2
x
−
4
y
+
3
z
=
6
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q76
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
A line with direction ratio
(
2
,
1
,
2
)
meets the lines
x
=
y
+
a
=
z
a
n
d
x
+
a
=
2
y
=
2
z
. The coordinates of the points of intersections are ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q75
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
A variable plane is at a distance
k
from origin and meets the coordinate axes at the points
A
,
B
,
C
respectively. then the locus of centroid of the
Δ
A
B
C
is ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q74
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane passing through the point
(
1
,
1
,
1
)
and having direction ratios
b
,
c
,
a
(
a
<
b
<
c
)
, where
a
,
b
,
c
are prime factors of
2001
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q73
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
If
P
(
0
,
1
,
0
)
a
n
d
Q
(
0
,
0
,
1
)
are two points in space, then the projection of
P
Q
on the plane
x
+
y
+
z
=
3
is ?
jeemain
math
class11
ch11
3d-geometry
coordinate-axes-and-planes
easy
q72
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
Distance of a point
P
(
→
c
)
from the the line
→
r
=
→
a
+
λ
→
b
is ?
jeemain
math
class11
ch11
3d-geometry
distance-between-two-points
easy
q71
answered
Jan 6, 2014
by
rvidyagovindarajan_1
1
answer
A vector
→
a
is parallel to the line of intersection of planes
P
1
containing vectors
ˆ
i
,
ˆ
i
+
ˆ
j
and
P
2
conataining vectors
ˆ
i
−
ˆ
j
,
ˆ
i
+
ˆ
k
. Then the angle between
→
a
and
ˆ
i
−
2
ˆ
j
+
2
ˆ
k
is?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q70
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
The vectors
→
a
,
→
b
,
→
c
→
d
be are such that
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
0
and
P
1
,
P
2
are two planes containing the pair of vectors
→
a
,
→
b
and
→
c
,
→
d
respectively, then the angle between the planes is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q69
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
A line passes through the points with position vectors are
ˆ
i
+
ˆ
j
−
2
ˆ
k
and
ˆ
i
−
3
ˆ
j
+
ˆ
k
. The position vector of a point on the line which is at a unit distance from the first point is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q68
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
If
→
a
,
→
b
,
→
c
are position vectors of three non collinear points
A
,
B
,
C
respectively, then the shortest distance of
A
from
B
C
is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
medium
q67
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
The distance of the point
(
1
,
1
,
1
)
from the plane passing through the points
(
2
,
1
,
1
)
,
(
1
,
2
,
1
)
a
n
d
(
1
,
1
,
2
)
is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
medium
q66
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
The line joining the points
6
→
a
−
4
→
b
−
5
→
c
and
−
4
→
c
and the line joining the points
−
→
a
−
2
→
b
−
3
→
c
and
→
a
+
2
→
b
−
5
→
c
Intersects at the point ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q65
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane having intercepts of
3
and
4
with
x
and
z
axes respectively and parallel to
y
axis is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
easy
q64
answered
Jan 5, 2014
by
rvidyagovindarajan_1
1
answer
If the lines
x
=
1
+
s
,
y
=
−
3
−
λ
s
,
z
=
1
+
λ
s
and
x
=
t
/
2
,
y
=
1
+
t
,
z
=
2
−
t
with parameters
s
a
n
d
t
respectively, are coplanar, then
λ
=
?
jeemain
math
class12
ch11
3d-geometry
coplanar-lines
difficult
q63
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane containing the lines
→
r
=
→
a
1
+
λ
→
b
a
n
d
→
r
=
→
a
2
+
μ
→
b
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q62
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane that contains the line
→
r
=
2
ˆ
i
+
λ
(
ˆ
j
−
ˆ
k
)
and
⊥
to the plane
→
r
.
(
ˆ
i
+
ˆ
k
)
=
3
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q61
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane through the point
(
1
,
2
,
−
1
)
and
⊥
to the line of intersection of the planes
→
r
.
(
3
ˆ
i
−
ˆ
j
+
ˆ
k
)
=
1
and
→
r
.
(
ˆ
i
+
4
ˆ
j
−
2
ˆ
k
)
=
2
is?
jeemain
math
class12
ch11
3d-geometry
medium
intersection-of-lines-and-planes
q60
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
If the position vector of the points
A
a
n
d
B
are
ˆ
i
−
ˆ
j
+
3
ˆ
k
and
3
ˆ
i
+
3
ˆ
j
+
3
ˆ
k
and the equation of a plane is
→
r
.
(
5
ˆ
i
+
2
ˆ
j
−
7
ˆ
k
)
+
9
=
0
, then the points
A
a
n
d
B
are?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
easy
q59
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane through origin and the line of intersection of the planes
→
r
.
→
a
=
λ
a
n
d
→
r
.
→
b
=
μ
is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
easy
q58
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
If
P
(
x
,
y
,
z
)
is a point on the line segment joining
Q
(
2
,
2
,
4
)
a
n
d
R
(
3
,
5
,
6
)
such that the projections of
→
O
P
on the coordinate axes are
13
5
,
19
5
,
26
5
respectively, then
P
divides
Q
R
in the ratio ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q56
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
If
P
is a point in space such that
O
P
=
12
and
→
O
P
is inclined with angle
45
∘
with
O
X
and
60
∘
with
O
Y
then the coordinates of
P
is ?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q55
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
If
P
(
3
,
2
,
−
4
)
,
Q
(
5
,
4
,
−
6
)
a
n
d
R
(
9
,
8
,
−
10
)
are collinear,then
R
divides
P
Q
in ratio?
jeemain
math
class11
ch12
3d-geometry
section-formula
easy
q54
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The length of
⊥
from origin to the plane passing through the point
→
a
and containing the line
→
r
=
→
b
+
λ
→
c
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q53
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane through the line of intersection of the planes
a
x
+
b
y
+
c
z
=
d
=
0
and
a
′
x
+
b
′
y
+
c
′
z
+
d
′
=
0
and parallel to the line
y
=
0
,
z
=
0
is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q52
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The line through the point
ˆ
i
+
3
ˆ
j
+
2
ˆ
k
and
⊥
to the lines
→
r
=
(
ˆ
i
+
2
ˆ
j
−
ˆ
k
)
+
λ
(
2
ˆ
i
+
ˆ
j
+
ˆ
k
)
and
→
r
=
(
2
ˆ
i
+
6
ˆ
j
+
ˆ
k
)
+
μ
(
ˆ
i
+
2
ˆ
j
+
3
ˆ
k
)
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q51
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The distance of the point
(
−
1
,
2
,
6
)
from the line through the point
(
2
,
3
,
−
4
)
along the vector
6
ˆ
i
+
3
ˆ
j
−
4
ˆ
k
is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q50
asked
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
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