Problem on the length of a vector

Consider a pyramid with square base formed by the points $(1,1,0), (1,-1, 0), (-1, 1, 0), (-1, -1, 0),$ and $(0,0,1)$. What is the length of each edge connecting the base to the apex?
• Solution

To find the length of an edge, we represent it as a vector and use the formula for the length of a vector.
Recall that
Thus, the vector starting at $(1,1,0)$ and ending at $(0,0,1)$ is given by $$(0,0,1) - (1,1,0) = (-1, -1, 1)$$
Recall that
Hence, the edge going from $(1,1,0)$ to $(0,0,1)$ has length $$\sqrt{(-1)^2 + (-1)^2 + 1^2} = \sqrt{3}.$$
The lengths of the 3 other edges connecting the base to the apex are the same because of a similar calculation.