What is the distance between #(–6, 3, 1) # and #(0, 4, –2) #?

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Answer 1 · 2016-07-02T07:42:22

The distance between #(-6,3,1)# and #(0,4,-2)# is#6.782#

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 #(-6,3,1)# and #(0,4,-2)# is

#sqrt((0-(-6))^2+(4-3)^2+(-2-1)^2)#

= #sqrt(6^2+1^2+(-3)^2)=sqrt(36+1+9)=sqrt46=6.782#