Find the distance between the points :
(i) A(5, 1, 2) and B(4, 6, -1)
(ii) P(1, -1, 3) and Q(2, 3, -5)
(iii) R(1, -3, 4) and S(4, -2, -3)
(iv) C(9, -12, -8) and the origin
Formula:
The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D=
(i) A(5, 1, 2) and B(4, 6, -1)
Here, (x1,y1,z1) = (5, 1, 2)
(x2,y2,z2)= (4, 6, -1)
Therefore,
D = 
= 
= 
=
Distance between points A and B is 
.
(ii) P(1, -1, 3) and Q(2, 3, -5)
Here, (x1,y1,z1)= (1, -1, 3)
(x2,y2,z2)= (2, 3, -5)
Therefore,
D = 
= 
= 
=
= 9
Distance between points P and Q are 9 units.
(iii) R(1, -3, 4) and S(4, -2, -3)
Here, (x1,y1,z1)= (1, -3, 4)
(x2,y2,z2)= (4, -2, -3)
Therefore,
D = 
= 
= 
=
Distance between points R and S is 
units.
(iv) C(9, -12, -8) and the origin
Coordinates of origin are (0, 0, 0)
Here, (x1,y1,z1)= (9, -12, -8)
(x2,y2,z2)= (0, 0, 0)
Therefore,
D = 
= 
= 
=
= 17
Distance between points C and origin is 17 units.