Introduction To Three Dimensional Geometry CBSE Questions & Answers

Introduction To Three Dimensional Geometry

This is Mathematics Class 11 Introduction to Three Dimensional Geometry CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A line making angles \({45^0}and{60^0}\) with the positive directions of the axis of x and y makes with the positive direction of Z axis , an angle of
  • A
    \({120^0}\)
  • B
    \({60^0}\)
  • C
    \({60^0}or120{^0}\)
    Correct
  • D
    \({45^0}\)
2
The coordinates of the point which divides the line segment joining the points ( 5 , 4, 2 ) and ( - 1 , - 2 , 4 ) in the ratio 2 : 3 externally is
  • A
    ( 13/5 , 8/5 , 14/5 )
  • B
    none of these
    Correct
  • C
    ( 17 , 16 , -2 )
  • D
    ( 17/5 , 16/5 , - 2/5 )
3
The angle between a line with direction ratios 2 : 2 : 1 and a line joining ( 3 , 1 , 4 ) to ( 7 , 2 , 12 )
  • A
    \(ta{n^{ - 1}}( - {2 \over 3})\)
  • B
    \(co{s^{ - 1}}({3 \over 2})\)
  • C
    none of these
  • D
    \(co{s^{ - 1}}({2 \over 3})\)
    Correct
4
Lines OA , OB are drawn from 0 with direction cosines proportional to \(<\) 1 , - 2 , - 1 \(>\) and \(<\) 3 , - 2 , 3 \(>\) respectively . The direction ratios of the normal to the plane AOB are
  • A
    \(<\) 4 , 3 , 2 \(>\)
  • B
    \(<\) - 4 , 3 , 2 \(>\)
  • C
    \(<\) - 4 , - 3 , 2 \(>\)
  • D
    \(<\) 4 , 3 , - 2 \(>\)
    Correct
5
The projections of a line segment on the coordinate are 1, 2, 4 and 3 respectively. The length of the line segment is
  • A
    13
    Correct
  • B
    16
  • C
    19
  • D
    15
6
The points A ( 5 , - 1 , 1 ) , B ( 7 , - 4 , 7 ) , C ( 1 , - 6 , 10 ) and D ( - 1 , - 3 , 4 ) are the vertices of
  • A
    square
  • B
    rectangle
  • C
    rhombus
    Correct
  • D
    none of these
7
If the projections of \(\overrightarrow {PQ} \) on OX , OY , OZ are respectively 12 , 3 and 4 , then the magnitude of \(\overrightarrow {PQ} \) is
  • A
    19
  • B
    13
    Correct
  • C
    144
  • D
    169
8
The centre of sphere passing through four points ( 0 , 0 , 0 ) , ( 0 , 2 , 0 ) , ( 1 , 0 , 0 ) and ( 0 , 0 , 4 ) is
  • A
    ( 1/2, 1 , 2 )
    Correct
  • B
    ( 1/2, 1 , - 2 )
  • C
    ( 1 , 1/2, 2 )
  • D
    ( -1/2 , 1 , 2 )
9
The ratio in which the line joining ( 2 , 4 , 5 ) ( 3 , 5 , - 4 ) is divided by the YZ – plane is
  • A
    it is 4 : - 3
  • B
    it is 3 : 2
  • C
    it is 2 : 3
  • D
    it is - 2 : 3
    Correct
10
The area of the triangle whose vertices are ( 1 , 2 , 3 ) , ( 2 , 5 , - 1 ) , ( - 1 , 1 , 2 ) is (sq. units)
  • A
    145
  • B
    165
  • C
    \({{\sqrt {155} } \over 2}\)
    Correct
  • D
    150
11
The direction ratios of a normal to the plane through ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , which makes an angle of \({\pi \over 4}withtheplanex + y = 3\)
  • A
    \(<\) 1, 1, \(\sqrt 2 \)\(>\)
    Correct
  • B
    \(<\) 1, 1, 2 \(>\)
  • C
    \(<\) 1, \(\sqrt 2 ,1\)\(>\)
  • D
    \(<\) \(\sqrt 2 ,1,1\) \(>\)
12
A tetrahedron has vertices at O ( 0 , 0 ,0 ), A ( 1 , 2, 1 ) , B ( 2 , 1 , 3 ) and C ( - 1 , 1 , 2 ) , then the angle between the faces OAB and ABC will be
  • A
    \(co{s^{ - 1}}\left( {{{19} \over {35}}} \right)\)
    Correct
  • B
    \({90^0}\)
  • C
    \({30^0}\)
  • D
    \(co{s^{ - 1}}\left( {{{17} \over {31}}} \right)\)
13
The equation of any plane parallel to y – axis
  • A
    ax + cz = 0 , \({a^2} + {c^2} \ne 0\)
  • B
    none of these
  • C
    ax + cz + d = 0 , \({a^2} + {c^2} \ne 0\)
    Correct
  • D
    y = d
14
An angle between two diagonals of a cube is
  • A
    \(co{s^{ - 1}}\left( {{1 \over {\sqrt 2 }}} \right)\)
  • B
    \(co{s^{ - 1}}\left( {{1 \over 3}} \right)\)
    Correct
  • C
    \(co{s^{ - 1}}\left( {{9 \over 5}} \right)\)
  • D
    none of these
15
The points P ( 0 , 0, 0 ) , Q ( 2 , 0 , 0 ) , R ( 1 , \(\sqrt 3 \), 0 ) and S ( 1 , \({1 \over {\sqrt 3 }},{{2\sqrt 2 } \over {\sqrt 3 }})\) lie
  • A
    in a plane at right angles to Z – axis
  • B
    in a line
  • C
    in XOY plane
  • D
    none of these
    Correct