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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 Three Dimensional Space

Subtopic

Coordinate Axes and Coordinate Planes in Three Dimensional Space under Introduction to Three Dimensional Geometry for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a point lies in the ZXZX-plane, its yy-coordinate is:

    A.

    11

    B.

    −1-1

    C.

    00

    D.

    Any positive number

  2. 2.

    What is the distance of the point (x,y,z)(x, y, z) from the origin?

    A.

    x+y+zx + y + z

    B.

    sqrtx2+y2\\sqrt{x^2 + y^2}

    C.

    sqrtx2+y2+z2\\sqrt{x^2 + y^2 + z^2}

    D.

    x2+y2+z2x^2 + y^2 + z^2

  3. 3.

    The Octant I is characterized by which signs?

    A.

    (+,+,+)(+, +, +)

    B.

    (−,−,−)(-, -, -)

    C.

    (+,−,+)(+, -, +)

    D.

    (−,+,+)(-, +, +)

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

Coordinates of a Point in Space

Subtopic

Coordinates of a Point in Space under Introduction to Three Dimensional Geometry for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the coordinates of the midpoint of the line segment joining the points A(2,4,6)A(2, 4, 6) and B(4,0,2)B(4, 0, 2).

    A.

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

    B.

    (3,2,4)(3, 2, 4)

    C.

    (6,4,8)(6, 4, 8)

    D.

    (3,4,2)(3, 4, 2)

  2. 2.

    Which of the following represents the general coordinates of any point lying on the yzyz-plane?

    A.

    (x,y,0)(x, y, 0)

    B.

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

    C.

    (x,0,z)(x, 0, z)

    D.

    (0,y,z)(0, y, z)

  3. 3.

    What is the distance of the point P(a,b,c)P(a, b, c) from the xx-axis?

    A.

    b2+c2\sqrt{b^2 + c^2}

    B.

    a2+c2\sqrt{a^2 + c^2}

    C.

    a2+b2\sqrt{a^2 + b^2}

    D.

    a2+b2+c2\sqrt{a^2 + b^2 + c^2}

Download the worksheet for Introduction to Three Dimensional Geometry - Coordinates of a Point in Space 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 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the distance between points Q(1,1,0)Q(1, 1, 0) and R(1,0,1)R(1, 0, 1).

    A.

    11

    B.

    22

    C.

    3\sqrt{3}

    D.

    2\sqrt{2}

  2. 2.

    What is the distance of point P(3,3,3)P(3, 3, 3) from the origin?

    A.

    33

    B.

    99

    C.

    333\sqrt{3}

    D.

    3\sqrt{3}

  3. 3.

    Find the distance between the points M(1,1,1)M(1, 1, 1) and N(2,1,1)N(2, 1, 1).

    A.

    11

    B.

    2\sqrt{2}

    C.

    3\sqrt{3}

    D.

    00

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 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the point dividing (3,4,5)(3, 4, 5) and (0,0,0)(0, 0, 0) internally in the ratio 2:12:1.

    A.

    (2,83,103)(2, \frac{8}{3}, \frac{10}{3})

    B.

    (1,43,53)(1, \frac{4}{3}, \frac{5}{3})

    C.

    (1.5,2,2.5)(1.5, 2, 2.5)

    D.

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

  2. 2.

    Determine the midpoint of the line joining (−2,−4,−6)(-2, -4, -6) and (−8,−10,−12)(-8, -10, -12).

    A.

    (−5,−7,−9)(-5, -7, -9)

    B.

    (−4,−6,−8)(-4, -6, -8)

    C.

    (−6,−8,−10)(-6, -8, -10)

    D.

    (−10,−14,−18)(-10, -14, -18)

  3. 3.

    The ratio in which the YZYZ-plane divides the segment joining (1,5,7)(1, 5, 7) and (−3,2,1)(-3, 2, 1) is:

    A.

    1:31:3 internally

    B.

    1:31:3 externally

    C.

    3:13:1 internally

    D.

    2:32:3 internally

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