Question

Find the distance between the following pairs of points:

(i) (2, 3, 5) and (4, 3, 1)

(ii) (-3, 7, 2) and (2, 4, -1)

(iii) (-1, 3, -4) and (1, -3, 4)

(iv) (2, -1, 3) and (-2, 1, 3).

Answer 1

(i) Let A $(2,3,5)$ and $B(4,3,1)$ be two points Then

$AB=\sqrt{(4-2{)}^2+(3-3{)}^2+(1-5{)}^2}$

= $\sqrt{4+0+16}=\sqrt{20}$

= $2\sqrt{5}$ units

(ii) Let A $(-3,7,2)$ and $B(2,4,-1)$ be two points. Then

$AB=\sqrt{[2-(-3){]}^2+(4-7{)}^2+(-1-2{)}^2}$

= $\sqrt{(2+3{)}^2+(4-7{)}^2+(-1-2{)}^2}$

= $\sqrt{25+9+9}=\sqrt{43}$ units

(iii) Let $A(-1,3,-4)$ and $B(1,-3,4)$ be two points. Then

$AB=\sqrt{[1-(-1){]}^2+(-3-3{)}^2+[4-(-4){]}^2}$

= $\sqrt{4+36+64}=\sqrt{104}=2\sqrt{26}$

(iv) Let $A(2,-1,3)$ and $B(-2,1,3)$ be two points. Then

$AB=\sqrt{(-2-2{)}^2+[1-(-1){]}^2+(3-3{)}^2}$

$\sqrt{(-2-2{)}^2+(1+1{)}^2+(3-3{)}^2}$

$\sqrt{16+4+0}=\sqrt{20}=2\sqrt{5}$ units