What is the distance between (13,-14,1)(13,−14,1) and (12,-21,6)(12,−21,6)?

1 Answer
Tony B
May 14, 2016

d=5sqrt(3)" "d=5√3 Exactly

d= 8.660" "d=8.660 to 3 decimal places

Explanation:

This is the coordinate system for 3-space. When it is broken down into projections onto the planes you end up with two triangles that are linked by a common side. Consequently we can turn to that good old favourite: Pythagoras.

Let the distance between points be dd

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2) d=√(x2−x1)2+(y2−y1)2+(z2−z1)2

d=sqrt( (12-13)^2+(-21-(-14))^2+(6-1)^2)d=√(12−13)2+(−21−(−14))2+(6−1)2

d=sqrt(75) = sqrt(5^2xx3)d=√75=√52×3
d=5sqrt(3)" "d=5√3 Exactly

d= 8.660" "d=8.660 to 3 decimal places

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