Problem

Find the distance between the points P(1,2,3) and Q(4,5,6) in 3d space.

Answer

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Answer

Simplify: \(D = \sqrt{9 + 9 + 9} = \sqrt{27}\)

Steps

Step 1 ：The formula for the distance between two points P\((x_1, y_1, z_1)\) and Q\((x_2, y_2, z_2)\) in 3D space is \(D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\)

Step 2 ：Substitute the respective values into the formula: \(D = \sqrt{(4-1)^2 + (5-2)^2 + (6-3)^2} = \sqrt{3^2 + 3^2 + 3^2}\)

Step 3 ：Simplify: \(D = \sqrt{9 + 9 + 9} = \sqrt{27}\)

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