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

1 Answer
Apr 6, 2018

Answer:

#sqrt(35)#

Explanation:

The (Euclidean) distance between two points #(x_1, y_1, z_1)# and #(x_2, y_2, z_2)# is given by the formula:

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

So for #(x_1, y_1, z_1) = (-6, 3, 1)# and #(x_2, y_2, z_2) = (-1, 4, -2)# the distance is:

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

#=sqrt(5^2+1^2+(-3)^2) = sqrt(25+1+9) = sqrt(35)#