Answer:
The distance between points P(x
1
,y
1
,z
1
) and Q(x
2
,y
2
,z
2
) is given by
PQ=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
+(z
2
−z
1
)
2
(i) Distance between points (2,3,5) and (4,3,1)
=
(4−2)
2
+(3−3)
2
+(1−5)
2
=
(2)
2
+(0)
2
+(−4)
2
=
4+16
=
20
= 2
5
(ii) Distance between points (−3,7,2) and (2,4,−1)
=
(2+3)
2
+(4−7)
2
+(−1−2)
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
+(−3−3)
2
+(4+4)
2
=
(2)
2
+(−6)
2
+(8)
2
=
4+36+64
=
104
=2
26
(iv) Distance between points (2,−1,3) and (−2,1,3)
=
(−2−2)
2
+(1+1)
2
+(3−3)
2
=
(−4)
2
+(2)
2
+(0)
2
=
16+4
=
20
= 2
5
