Vidaara.orgClass 11 · Mathematics
CodeVID-M11-11-CT
Introduction to Three Dimensional Geometry — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The number of octants is:
- A.$4$
- B.$8$
- C.$6$
- D.$2$
2.
The distance of $(a,b,c)$ from the origin is:
- A.$a+b+c$
- B.$\sqrt{a^2+b^2+c^2}$
- C.$a^2+b^2+c^2$
- D.$abc$
3.
The midpoint is the ___ of the coordinates.
- A.sum
- B.average
- C.product
- D.difference
4.
The coordinates of the origin are:
- A.$(0,0,0)$
- B.$(1,1,1)$
- C.$(0,0,1)$
- D.$(1,0,0)$
5.
The distance between $(0,0,0)$ and $(3,4,0)$ is:
- A.$7$
- B.$5$
- C.$\sqrt7$
- D.$12$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
In which octant does $(1,2,3)$ lie?
7.
Find the distance between $(1,2,3)$ and $(4,6,3)$.
8.
Find the midpoint of $(1,2,3)$ and $(5,6,7)$.
9.
What is the $z$-coordinate of any point on the $xy$-plane?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Write the coordinates of the projection of $(2,3,4)$ on the $xy$-plane.
11.
Find the distance between $(2,3,5)$ and $(4,3,1)$.
12.
Find the point dividing $(2,3,4)$ and $(6,7,8)$ in the ratio $3:1$.
13.
In which octant does $(-1,-2,-3)$ lie?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
State the octant of each point: $(1,-2,3),\ (-1,2,-3),\ (-2,-3,-1)$.
15.
Show that the points $A(1,2,3),\ B(-1,-2,-1),\ C(2,3,2),\ D(4,7,6)$ form a parallelogram.
Answer Key
Section A — Multiple Choice Questions
- (B) $8$
- (B) $\sqrt{a^2+b^2+c^2}$
- (B) average
- (A) $(0,0,0)$
- (B) $5$
Section B — Short Answer (2 marks)
- The first octant.
- $5$.
- $(3,4,5)$.
- $0$.
Section C — Short Answer (3 marks)
- $(2,3,0)$.
- $2\sqrt5$.
- $(5,6,7)$.
- The seventh octant.
Section D — Long Answer (5 marks)
- IV, VI and VII respectively.
- A parallelogram (diagonals bisect each other at $(1.5,2.5,2.5)$).
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