Question

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

Answer 1

The distance between two points (x₁,y₁,z₁) and (x₂,y₂,z₂) is given by

Distance 

(i) A(5, 1, 2) and B(4, 6, -1)

Here (x₁, y₁, z₁) = (5, 1, 2) and (x₂, y₂, z₂) = (4, 6, -1)

Now,

Distance between A and B is √35 units

(ii) P(1, -1, 3) and Q(2, 3, -5)

Here (x₁, y₁, z₁) = (1, -1, 3) and (x₂, y₂, z₂) = (2, 3, -5)

Distance between P and Q is 9 units

(iii) R(1, -3, 4) and S(4, -2, -3)

Here (x₁, y₁, z₁) = (1, -3, 4) and (x₂, y₂, z₂) = (4, -2, -3)

Distance between R and S is √59 units

(iv) C(9, -12, -8) and the origin

Here (x₁, y₁, z₁) = (9, -12, -8) and (x₂, y₂, z₂) = (0, 0, 0)

Distance between C and Origin is 17 units.