What is the distance between #(8,1,-4)# and #(-3,6-2)#?

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Answer 1 · 2016-06-09T12:19:25

The distance between #(8,1,-4)# and #(-3,6,-2)# is #12.2475#

In a two dimensional plane, distance between two points #(x_1,y_1)# and #(x_2,y_2)# is given by

#sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

and in three dimensional space, distance between two points #(x_1,y_1,z_1)# and #(x_2,y_2,z_2)# is given by

#sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

Hence, the distance between #(8,1,-4)# and #(-3,6,-2)# is

#sqrt((8-(-3))^2+(1-6)^2+(-4-(-2))^2)#

= #sqrt(11^2+(-5)^2+(-2)^2)=sqrt(121+25+4)=sqrt150#

= #sqrt(2xx3xx5xx5)=5sqrt6=5xx2.4495=12.2475#