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.