# NCERT Class 11-Math՚s: Chapter – 12 Introduction to Three Dimensional Geometry Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 12.3 EXERCISE

### Short Answer Type

**Question 1**:

Locate the following points:

(i) (1, – 1,3) ,

(ii) (– 1,2, 4)

(iii) (– 2, – 4, – 7)

(iv) (– 4,2, – 5) .

**Answer**:

(i)

(ii)

(iii)

(iv)

**Question 2**:

Name the octant in which each of the following points lies.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

**Answer**:

(i) 1^{st} octant

(ii) 4^{th} octant

(iii) octant

(iv) octant

(v) 2^{nd} octant

(vi) 3^{rd} octant

(vii) octant

(viii) octant

**Question 3**:

Let A, B, C be the feet of perpendiculars from a point P on axis respectively. Find the coordinates of A, B and C in each of the following where the point P is:

(i)

(ii)

(iii)

**Answer**:

(i)

(ii)

(iii)

**Question 4**:

Let A, B, C be the feet of perpendiculars from a point P on the and planes respectively. Find the coordinates of A, B, C in each of the following where the point P is

(i) (3,4, 5)

(ii) (– 5,3, 7)

(iii) (4, – 3, – 5) .

**Answer**:

(i)

(ii)

(iii)

**Question 5**:

How far apart are the points and ?

**Answer**:

**Question 6**:

Find the distance from the origin to .

**Answer**:

**Question 7**:

Show that if , then the point is at a distance 1 unit from the origin.

**Answer**:

Given;

Distance of the point from origin is:-

When the distance of that point from origin will be 1 unit.