Question

Compute the distance between (9,-5,4) and (-10,3,4)

Answer 1

~20.6155

Explanation:

To compute distance between two points, we can get the vector from one to the other by subtracting them and then computing the length of the vector.

The length of a vector V is:

`|V| = \sqrt{\sum_(i=1)^n v_i^2}\\`

The vector is:

(9, -5. 4) - (-10, 3, 4) = (9 + 10, -5 - 3, 4 - 4) = (19, -8, 0)

So the length is:

`√(19^2 + (-8)^2) = √(361 + 64) = √(425) = √(5\cdot 5\cdot 17) = 5√(17) \approx 20.6155281281`