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
The distance between the planes \(\vec r.\hat n = {p_{1}}and\) \(\vec r.( - \hat n) = {p_{2}}is\)
  • A
    \({p_1} + {p_2}\)
    Correct
  • B
    \(\left| {{p_1} - {p_2}} \right|\)
  • C
    none of these
  • D
    \({p_2} - {p_1}\)
2
The point equidistant from the points ( 0 , 0 , 0 ) , ( 1 , 0 , 0 ) , ( 0 , 2 , 0 ) , and ( 0 , 0 , 3 ) is
  • A
    none of these
  • B
    ( - 1/2 ,- 1 , - 3/2 )
  • C
    ( 1 , 2 ,3 )
  • D
    ( 1/2 , 1 , 3/2 )
    Correct
3
The plane x + y = 0 is
  • A
    none of these
  • B
    parallel to z – axis
  • C
    passes through z – axis
    Correct
  • D
    perpendicular to z – axis
4
The points ( 1 , 1 , 0 ) , ( 0 , 1 , 1 ) , ( 1 , 0 , 1 ) , and ( 2/3 , 2/3 , 2/3 ) are
  • A
    non coplanar
  • B
    none of these
  • C
    coplanar
    Correct
  • D
    the vertices of a parallelogram
5
the lines The lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}and{{x - 1} \over 3} = {{y - 2} \over 4} = {{z - 3} \over 5}are\)
  • A
    parallel
  • B
    none of these
  • C
    skew
  • D
    intersecting
    Correct
6
The lines \({l_1}and{l_2}\) intersect . The shortest distance between them is
  • A
    zero
    Correct
  • B
    negative
  • C
    infinity
  • D
    positive
7
Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is
  • A
    it is 1/6
    Correct
  • B
    it is 1/4
  • C
    it is 1/3
  • D
    it is 1/2
8
A , B C and D are four points in spaces such that AB = BC = CD = DA . Then ABCD is a
  • A
    skew quadrilateral
  • B
    rhombus
  • C
    rectangle
  • D
    nothing can be said
    Correct
9
The foot of perpendicular from (\(\alpha {\rm{ }},\beta {\rm{ }},{\rm{ }}\gamma \))on Y axis is
  • A
    ( 0 , 0 , 0 )
  • B
    ( 0 , α , 0 )
  • C
    none of these
  • D
    ( 0 , \(\beta \) , 0 )
    Correct
10
The equation \(\vec r = \lambda \hat j\) represents
  • A
    the Y axis
    Correct
  • B
    the Z axis
  • C
    the plane y = 0
  • D
    the X axis
11
The equation \(\vec r = \lambda \widehat {i} + \mu \widehat {k} \) represents
  • A
    the Y axis
  • B
    the X axis
  • C
    the Z axis
  • D
    the plane y = 0
    Correct
12
The centre of the sphere , which passes through ( a , 0 , 0 ) , ( 0 , b , 0 ) ( 0 , 0 , c ) and ( 0 , 0 ,0 ) is abc \( \ne \) 0
  • A
    ( a/2 , 0 ,0 )
  • B
    ( 0 , b/2 , 0 )
  • C
    ( 0 , 0 , c/2 )
  • D
    ( a/2 , b/2 , c/2 )
    Correct
13
The equations y axis are
  • A
    x = 0 , z = o
    Correct
  • B
    x = 0 , y = 0
  • C
    x = 0 , y = 0 , z = 0
  • D
    y = 0 , z = 0
14
The equation \(\vec r = \lambda \widehat {j} + \mu \widehat {k} \) represents
  • A
    the Z axis
  • B
    the plane x = 0
    Correct
  • C
    the X axis
  • D
    the Y axis
15
A sphere through three non – collinear points A, B, and C is smallest when its centre is
  • A
    in the plane ABC
    Correct
  • B
    at centroid of triangle ABC
  • C
    at origin
  • D
    none of these