What is the distance between (0, 0, 8) (0,0,8) and (8, 6, 2) (8,6,2)?

1 Answer
SagarStudy
Jan 10, 2016

2sqrt(34)2√34 units.

Explanation:

The distance formula for Cartesian coordinates is

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2d=√(x2−x1)2+(y2−y1)2+(z2−z1)2
Where x_1, y_1,z_1x1,y1,z1, andx_2, y_2,z_2x2,y2,z2 are the Cartesian coordinates of two points respectively.
Let (x_1,y_1,z_1)(x1,y1,z1) represent (0,0,8)(0,0,8) and (x_2,y_2,z_2)(x2,y2,z2) represent (8,6,2)(8,6,2).
implies d=sqrt((8-0)^2+(6-0)^2+(2-8)^2⇒d=√(8−0)2+(6−0)2+(2−8)2
implies d=sqrt((8)^2+(6)^2+(-6)^2⇒d=√(8)2+(6)2+(−6)2
implies d=sqrt(64+36+36⇒d=√64+36+36
implies d=sqrt(136⇒d=√136
implies d=2sqrt(34⇒d=2√34 units

Hence the distance between the given points is 2sqrt(34)2√34 units.

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