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CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 11 - MCQExams.com
CBSE
Class 11 Engineering Maths
Introduction To Three Dimensional Geometry
Quiz 11
If
P
(
x
,
y
,
z
)
is a point on the line segment joining
Q
(
2
,
2
,
4
)
and
R
(
3
,
5
,
6
)
such that the projections of
O
P
on the axis are
13
5
,
19
5
,
26
5
respectively, then
P
divides
Q
R
in the ratio
Report Question
0%
1
:
2
0%
3
:
2
0%
2
:
3
0%
1
:
3
Explanation
Since,
¯
O
P
has projections
13
5
,
19
5
,
26
5
on the coordinate axes
∴
¯
O
P
=
13
5
ˆ
i
+
19
5
ˆ
j
+
26
5
ˆ
k
Suppose
P
divides the line segment joining of
Q
(
2
,
2
,
4
)
and
R
(
3
,
5
,
6
)
in the ratio
λ
:
1
then the position vector of
P
is
(
3
λ
+
2
λ
+
1
)
ˆ
i
+
(
5
λ
+
2
λ
+
1
)
ˆ
j
+
(
6
λ
+
4
λ
+
1
)
ˆ
k
∴
13
5
ˆ
i
+
19
5
ˆ
j
+
26
5
ˆ
k
=
(
3
λ
+
2
λ
+
1
)
ˆ
i
+
(
5
λ
+
2
λ
+
1
)
ˆ
j
+
(
6
λ
+
4
λ
+
1
)
ˆ
k
⇒
λ
=
3
/
2
∴
Required ratio in which
P
divides
Q
R
is
3
:
2
The points
A
(
1
,
2
,
3
)
;
B
−
(
−
1
,
−
2
,
−
1
)
;
C
(
2
,
3
,
2
)
and
D
(
4
,
7
,
6
)
form
Report Question
0%
Square
0%
Rectangle
0%
Parallelogram
0%
Rhombus
Find the coordinates of the points which trisect the line segment AB, given that
A =( 2,1 , - 3 ) and B =( 5 , - 8,3 ).
Report Question
0%
(
3
,
2
,
−
1
)
;
(
4
,
5
,
−
1
)
0%
(
3
,
−
2
,
−
1
)
;
(
4
,
−
5
,
1
)
0%
(
3
,
−
2
,
1
)
;
(
−
4
,
5
,
−
1
)
0%
(
3
,
−
2
,
−
1
)
;
(
4
,
5
,
−
1
)
30 consider at three dimensional figure represented by
x
y
z
2
=
2
, then its minimum distance from origin is
Report Question
0%
2
0%
4
0%
3
0%
1
The distances of the point
P
(
1
,
2
,
3
)
from the coordinates axes are:
Report Question
0%
√
13
,
√
10
,
√
5
0%
√
11
,
√
10
,
√
5
0%
√
13
,
√
20
,
√
15
0%
√
23
,
√
10
,
√
5
If O and O' are circumcenter and orthocenter of a
Δ
A
B
C
where
¯
O
A
+
¯
O
B
+
¯
O
C
is
λ
¯
O
O
′
then the value of
λ
is
Report Question
0%
1
0%
2
0%
3
0%
4
The distance between the orthocentre and circumcentre of the triangle formed by the points
(
1
,
2
,
3
)
,
(
3
,
−
1
,
5
)
,
(
4
,
0
,
−
3
)
is
Report Question
0%
√
66
2
0%
√
17
2
0%
√
55
2
0%
√
37
2
In the
x
y
−
p
l
a
n
e
, the length of the shortest from
(
0
,
0
)
to
(
12
,
16
)
that does not go inside the circle
(
x
−
6
)
2
+
(
y
+
8
)
2
=
25
is
Report Question
0%
10
√
3
0%
10
√
5
0%
10
√
3
+
5
π
3
0%
10
+
5
π
If
R
divides the line segment joining
P
(
2
,
3
,
4
)
and
Q
(
4
,
5
,
6
)
in the ratio
−
3
:
2
, then the parameter which represent
R
is
Report Question
0%
3
0%
2
0%
1
0%
−
1
Explanation
x
=
−
3
×
4
+
2
×
2
−
1
y
=
−
3
×
5
+
2
×
3
−
1
x
=
−
12
+
4
−
1
y
=
−
15
+
6
−
1
x
=
8
y
=
9
z
=
−
3
×
6
+
2
×
4
−
1
=
−
10
−
1
z
=
10
R
=
(
8
,
9
,
10
)
Consider at three dimensional figure represented by
x
y
z
2
=
2
, then its minimum distance from origin is
Report Question
0%
2
0%
4
0%
6
0%
8
The point which is equidistant from the points
(
−
1
,
1
,
3
)
,
(
2
,
1
,
2
)
,
(
0
,
5
,
6
)
and
(
3
,
2
,
2
)
is
Report Question
0%
(
−
1
,
3
,
4
)
0%
(
3
,
1
,
4
)
0%
(
1
,
3
,
4
)
0%
$$(4,1,3)$4
Minimum distance between the curves
y
2
=
4
x
&
x
2
+
y
2
−
12
x
+
31
=
0
is -
Report Question
0%
√
21
0%
√
26
−
√
5
0%
√
20
−
√
5
0%
√
21
−
√
5
Let
A
(
2
,
3
,
5
)
,
B
(
−
1
,
3
,
2
)
and
C
(
λ
,
5
,
μ
)
are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that
B
E
:
E
C
=
1
:
2.
Project of
BA
on
BC
Report Question
0%
23
√
33
0%
√
33
24
0%
24
√
33
0%
N
o
n
e
o
f
t
h
e
s
e
If A = (2,-3,1), B = (3,-4,6) and C is a point of trisection of AB, then
C
y
Report Question
0%
11
3
0%
-11
0%
10
3
0%
−
11
3
The coordinates of the orthocentre of the triangle that has the coordinates of mid points of its sides as (0 , 0) (1 , 2) and ( -6 , 3) is :
Report Question
0%
(0 , 0)
0%
(-4 , 5)
0%
(-5 , 5)
0%
(-4 , 4)
Let
A
(
2
,
3
,
5
)
,
B
(
−
1
,
3
,
2
)
and
C
(
λ
,
5
,
μ
)
are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that
B
E
:
E
C
=
1
:
2.
Equation of plane containing triangle ABC
Report Question
0%
x
+
y
+
3
=
0
0%
x
−
z
−
3
=
0
0%
x
−
z
+
3
=
0
0%
x
−
y
+
3
=
0
Perpendicular distance from the origin to the line joining the points
(
a
cos
θ
,
a
sin
θ
)
(
a
cos
θ
,
a
sin
θ
)
is
Report Question
0%
2
a
cos
(
θ
−
ϕ
)
0%
a
cos
(
θ
−
ϕ
2
)
0%
4
a
cos
(
θ
−
ϕ
2
)
0%
a
cos
(
θ
+
ϕ
2
)
Consider a variable plane
l
x
+
m
y
+
n
z
=
k
(
k
>
0
)
a
n
d
l
,
m
,
n
are direction cosines of normal of the plane. Let the given plane intersects the co-ordinate axes at A,B and C, then the minimum area of
△
A
B
C
is _______.
Report Question
0%
3
√
3
k
2
2
0%
3
√
3
k
2
4
0%
3
√
3
k
2
0%
12
√
3
k
2
The shortest distance between the point
(
3
2
,
0
)
and the curve
y
=
√
x
,
(
x
>
0
)
, is:
Report Question
0%
3
2
0%
√
3
2
0%
√
5
2
0%
5
4
Q, R, S are the points
(
−
2
,
−
1
)
,
(
0
,
3
)
(
4
,
0
)
respectively. Then the coordinates of P such that PQRS is a parallelogram is ________________.
Report Question
0%
(
2
,
−
6
)
0%
(
−
6
,
2
)
0%
(
2
,
−
4
)
0%
(
−
3
,
2
)
If
A
=
(
1
,
2
,
3
)
and
B
(
3
,
5
,
7
)
and P, Q are the points on AB such that AP
=
PQ
≠
QB, then the mid point of PQ is?
Report Question
0%
(
2
,
3
,
5
)
0%
(
2
,
7
2
,
5
)
0%
(
2
,
4
,
5
)
0%
(
4
,
7
,
0
)
If
A
=
(
1
,
−
2
,
−
1
)
,
B
=
(
4
,
0
,
−
3
)
;
C
=
(
1
,
2
,
−
1
)
and
D
=
(
2
,
−
4
,
−
5
)
, then the distance between AB and CD is?
Report Question
0%
2
3
0%
4
3
0%
3
2
0%
5
3
The equation of plane which is passing through the point
(
1
,
2
,
3
)
and which is at maximum distance from the point
(
−
1
,
0
,
2
)
is
Report Question
0%
2
x
+
2
y
+
z
=
9
0%
2
x
+
z
=
5
0%
3
x
+
y
−
z
=
2
0%
none of these
The distance of the point
(
2
,
1
,
−
1
)
from the line
x
−
1
2
=
y
+
1
1
=
z
−
3
−
3
measured parallel to the plane
x
+
2
y
+
z
=
4
is
Report Question
0%
√
10
0%
√
20
0%
√
5
0%
√
30
A line passes through two points A(2, -3, -1) and B(8, -1, 2) the coordinates of a point on this line nearer to the origin at a distance of 14 units from A are
Report Question
0%
(14 , 1, 5)
0%
(-10, -7, -7)
0%
(10 , 7, 7)
0%
(-14, -1, -5)
If
λ
is the length of any edge of a regular tetrahedron, then the distance of any vertex form the opposite face is-
Report Question
0%
2
3
λ
2
0%
√
2
3
λ
0%
√
2
3
λ
0%
N
o
n
e
o
f
t
h
e
s
e
Explanation
I
n
30
0
−
60
0
−
90
0
−
s
i
d
e
i
s
i
n
r
a
t
i
o
,
1
:
√
3
:
2
In regular tetraheron, height (h)
5
√
2
3
a
n
d
s
i
d
e
,
s
=
λ
∴
λ
=
√
2
3
λ
The distance of the point
(
2
,
3
)
form the line
x
−
2
y
+
5
=
0
measured in a direction parallel to the line
x
−
3
y
=
0
is
Report Question
0%
2
√
10
0%
√
10
0%
2
√
5
0%
N
o
n
e
o
f
t
h
e
s
e
If
A
=
(
1
,
−
2
,
−
1
)
,
B
=
(
4
,
0
,
−
3
)
,
C
=
(
1
,
2
,
−
1
)
,
D
=
(
2
,
−
4
,
−
5
)
, then distance between A B and CD is
Report Question
0%
1
3
0%
2
3
0%
1
0%
4
3
A
(
1
,
−
1
,
−
3
)
,
B
(
2
,
1
,
−
2
)
&
(
−
5
,
2
,
−
6
)
are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is:
Report Question
0%
√
10
/
4
0%
3
√
10
/
4
0%
√
10
0%
None
If x-coordinates of a point P on the joining the points
Q
(
2
,
2
,
1
)
and
R
(
5
,
1
,
−
2
)
is 4, then the z-coordinates of P is
Report Question
0%
-2
0%
-1
0%
1
0%
2
0:0:1
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10
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13
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15
16
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0
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Incorrect : 0
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