calculate distance between two points in 3D space
Check the final answer first, then review the worked steps.
Problem
calculate distance between two points in 3D space
Step-by-step solution
The distance between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$. For problem 9: $\sqrt{(1-4)^2 + (0-(-6))^2 + (1-0)^2} = \sqrt{(-3)^2 + 6^2 + 1^2} = \sqrt{9+36+1} = \sqrt{46}$. For problem 10: $\sqrt{(0-8)^2 + (0-7)^2 + (0-(-2))^2} = \sqrt{(-8)^2 + (-7)^2 + 2^2} = \sqrt{64+49+4} = \sqrt{117} = 3\sqrt{13}$.
Answer
9: \sqrt{46}, 10: 3\sqrt{13}