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

Question 1:

Locate the following points:

(i) (1, – 1,3) ,

(ii) (– 1,2, 4)

(iii) (– 2, – 4, – 7)

(iv) (– 4,2, – 5) .

(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)

(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)

(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) .

(i)

(ii)

(iii)

Question 5:

How far apart are the points and ?

Question 6:

Find the distance from the origin to .

Question 7:

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