# NCERT Class 11-Math's: Chapter –12 Introduction to Three Dimensional Geometry Part 7

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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) 1st octant

(ii) 4th octant

(iii) octant

(iv) octant

(v) 2nd octant

(vi) 3rd 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.

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