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

Formula: The distance between two points (x₁,y₁,z₁) and (x_2,y₂,z₂) is given by

D = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)

(i) A(5, 1, 2) and B(4, 6, -1) 

Here, (x₁,y₁,z₁) = (5, 1, 2) 

(x₂,y₂,z₂)= (4, 6, -1) 

Therefore,

Distance between points A and B is . 

\(\sqrt{35}\)

(ii) P(1, -1, 3) and Q(2, 3, -5) 

Here, (x₁,y₁,z₁)= (1, -1, 3) 

(x₂,y₂,z₂)= (2, 3, -5) 

Therefore,

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,

Distance between points R and S is \(\sqrt{59}\) 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,

Distance between points C and origin is 17 units.