Answer :

Formula:


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


D=


(i) A(5, 1, 2) and B(4, 6, -1)


Here, (x1,y1,z1) = (5, 1, 2)


(x2,y2,z2)= (4, 6, -1)


Therefore,


D =


=


=


=


Distance between points A and B is .


(ii) P(1, -1, 3) and Q(2, 3, -5)


Here, (x1,y1,z1)= (1, -1, 3)


(x2,y2,z2)= (2, 3, -5)


Therefore,


D =


=


=


= = 9


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,


D =


=


=


=


Distance between points R and S is 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,


D =


=


=


= = 17


Distance between points C and origin is 17 units.


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