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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)

Solution
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The distance between points P(x1,y1,z1) and Q(x2,y2,z2) is given by
PQ= (x2x1)2+(y2y1)2+(z2z1)2
(i) Distance between points (2,3,5) and (4,3,1)
= (42)2+(33)2+(15)2
= (2)2+(0)2+(4)2
= 4+16
= 20
= 25
(ii) Distance between points (3,7,2) and (2,4,1)
= (2+3)2+(47)2+(12)2
= (5)2+(3)2+(3)2
= 25+9+9
= 43
(iii) Distance between points (1,3,4) and (1,3,4)
= (1+1)2+(33)2+(4+4)2
= (2)2+(6)2+(8)2
= 4+36+64=104
=226
(iv) Distance between points (2,1,3) and (2,1,3)
= (22)2+(1+1)2+(33)2
= (4)2+(2)2+(0)2
= 16+4
= 20
= 25

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