Vidaara.orgClass 11 · Mathematics
CodeVID-M11-11-DST-01
Distance Formula in 3-D — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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 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.$abc$
2.
The distance between $(0,0,0)$ and $(3,4,0)$ is:
- A.$7$
- B.$5$
- C.$\sqrt7$
- D.$12$
3.
The distance between $(1,1,1)$ and $(1,1,4)$ is:
- A.$2$
- B.$3$
- C.$4$
- D.$\sqrt3$
4.
The distance of $(2,3,6)$ from the origin is:
- A.$6$
- B.$7$
- C.$11$
- D.$\sqrt{11}$
5.
The 3-D distance formula uses:
- A.$2$ differences
- B.$3$ differences
- C.$1$ difference
- D.$4$ differences
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the distance between $(1,2,3)$ and $(4,6,3)$.
7.
Find the distance of $(1,2,2)$ from the origin.
8.
Find the distance between $(0,0,0)$ and $(2,3,6)$.
9.
Find the distance between $(1,0,0)$ and $(0,1,0)$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the distance between $(2,3,5)$ and $(4,3,1)$.
11.
Show that $(0,7,10),(-1,6,6),(-4,9,6)$ form an isosceles triangle.
12.
Find the distance between $(a,b,c)$ and $(-a,-b,-c)$.
13.
Are the points $(1,2,3),(2,3,4),(3,4,5)$ collinear?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Show that the points $A(1,2,3),\ B(-1,-2,-1),\ C(2,3,2),\ D(4,7,6)$ form a parallelogram.
15.
Find the point on the $y$-axis equidistant from $A(3,1,2)$ and $B(5,5,2)$.
Answer Key
Section A — Multiple Choice Questions
- (B) $\sqrt{a^2+b^2+c^2}$
- (B) $5$
- (B) $3$
- (B) $7$
- (B) $3$ differences
Section B — Short Answer (2 marks)
- $5$.
- $3$.
- $7$.
- $\sqrt2$.
Section C — Short Answer (3 marks)
- $2\sqrt5$.
- Isosceles ($AB=BC=\sqrt{18}$).
- $2\sqrt{a^2+b^2+c^2}$.
- Yes (collinear).
Section D — Long Answer (5 marks)
- A parallelogram (diagonals bisect each other at $(1.5,2.5,2.5)$).
- $(0,5,0)$.
Generated by Vidaara.org · Assignment VID-M11-11-DST-01 · vidaara.org