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Introduction to Three-Dimensional Geometry

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Coordinate Axes and Coordinate Planes in 3D

Subtopic

Coordinate Axes and Coordinate Planes in 3D under Introduction to Three-Dimensional Geometry for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If P(x,y,z)P(x, y, z) is a point such that x>0,y>0,z<0x > 0, y > 0, z < 0, then PP lies in:

    A.

    Octant I

    B.

    Octant V

    C.

    Octant VI

    D.

    Octant II

  2. 2.

    The point (−1,−2,−3)(-1, -2, -3) lies in the:

    A.

    Octant VI

    B.

    Octant VII

    C.

    Octant VIII

    D.

    Octant III

  3. 3.

    How many coordinate axes are there in a three-dimensional rectangular Cartesian coordinate system?

    A.

    2

    B.

    3

    C.

    4

    D.

    8

Download the worksheet for Introduction to Three-Dimensional Geometry - Coordinate Axes and Coordinate Planes in 3D to practice offline. It includes additional chapter-level practice questions.

Coordinates of a Point

Subtopic

Coordinates of a Point under Introduction to Three-Dimensional Geometry for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    A point where x>0,y<0,z>0x > 0, y < 0, z > 0 is in which octant?

    A.

    Octant I

    B.

    Octant II

    C.

    Octant III

    D.

    Octant IV

  2. 2.

    Find the distance of the point (2,0,0)(2, 0, 0) from the zz-axis.

    A.

    00

    B.

    22

    C.

    44

    D.

    None of these

  3. 3.

    The point (−2,−3,−4)(-2, -3, -4) lies in Octant:

    A.

    III

    B.

    VII

    C.

    V

    D.

    VIII

Download the worksheet for Introduction to Three-Dimensional Geometry - Coordinates of a Point to practice offline. It includes additional chapter-level practice questions.

Distance between Two Points

Subtopic

Distance between Two Points under Introduction to Three-Dimensional Geometry for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the distance between (1,1,1)(1, 1, 1) and (3,3,3)(3, 3, 3).

    A.

    2

    B.

    12\sqrt{12}

    C.

    6

    D.

    4

  2. 2.

    Determine the distance between the points (2,0,0)(2, 0, 0) and (0,2,2)(0, 2, 2).

    A.

    232\sqrt{3}

    B.

    6

    C.

    4

    D.

    6\sqrt{6}

  3. 3.

    The distance of the point (p,q,r)(p, q, r) from the origin is:

    A.

    p+q+rp+q+r

    B.

    p2+q2+r2p^2+q^2+r^2

    C.

    p2+q2+r2\sqrt{p^2+q^2+r^2}

    D.

    ∣p+q+r∣|p+q+r|

Download the worksheet for Introduction to Three-Dimensional Geometry - Distance between Two Points to practice offline. It includes additional chapter-level practice questions.

Section Formula

Subtopic

Section Formula under Introduction to Three-Dimensional Geometry for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The centroid of a triangle with vertices (0,0,0)(0, 0, 0), (1,2,3)(1, 2, 3), and (−1,−2,−3)(-1, -2, -3) is:

    A.

    (0,0,0)(0, 0, 0)

    B.

    (1,1,1)(1, 1, 1)

    C.

    (1/3,2/3,1)(1/3, 2/3, 1)

    D.

    (0,1,2)(0, 1, 2)

  2. 2.

    In what ratio does the xzxz-plane divide the line segment joining (1,4,5)(1, 4, 5) and (2,8,10)(2, 8, 10)?

    A.

    1:21:2 internally

    B.

    1:21:2 externally

    C.

    2:12:1 externally

    D.

    4:84:8 internally

  3. 3.

    The midpoint of the line segment joining (a+b,b+c,c+a)(a+b, b+c, c+a) and (a−b,c−b,a−c)(a-b, c-b, a-c) is:

    A.

    (a,2c2,a)(a, \frac{2c}{2}, a)

    B.

    (a,c,a)(a, c, a)

    C.

    (b,c,a)(b, c, a)

    D.

    (a,b,c)(a, b, c)

Download the worksheet for Introduction to Three-Dimensional Geometry - Section Formula to practice offline. It includes additional chapter-level practice questions.

Introduction to Three-Dimensional Geometry - Class 11 Maths (ICSE) | Krit.club