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Class 11 Introduction to Three-dimensional Geometry worksheet
CBSE Mathematics. Octants, coordinate planes, distance between points in space. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The point (−2, 9, 2) lies in octant:
- II
- VI
- VIII
- VII
Answer
(a) II
signs (−, +, +)
- 2.
The point (−8, 0, −2) lies on:
- the xz-plane
- the z-axis
- the yz-plane
- the x-axis
Answer
(a) the xz-plane
look at which coordinates are zero
- 3.
The distance between (3, 4, 8) and (2, −8, 20) is:
- 17
- 18
- 289
- 25
Answer
(a) 17
√(1² + 12² + 12²) = √289
Section B · short answer
- 4.
Find the distance between (1, 8, 7) and (4, 5, −2).
Answer
3√11
√(3² + (−3)² + (−9)²) = √99
- 5.
Show that the points A(1, 0, −8), B(0, 2, −6) and C(−3, 8, 0) are collinear.
Answer
AB = 3, BC = 9, AC = 12; AB + BC = AC, so they are collinear
find the three distances
Section C · long answer
- 6.
A triangle has vertices A(8, 1, −6), B(5, −3, −4) and C(1, 8, 5). Find AB, BC and CA. Is the triangle right-angled? Is it isosceles?
Answer
AB = √29, BC = √218, CA = √219. Not right-angled. Not isosceles.
AB² = 29, BC² = 218, CA² = 219
Fresh sheets for your child
In the app, every Introduction to Three-dimensional Geometry sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.