The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
First, we find the vector between the two points by vector sum:
[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]
[tex]\vec r = (- 5, - 9, - 4)[/tex]
The distance between the two points is found by the following Pythagorean expression:
[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]
d ≈ 11.1
And the midpoint is found by linear algebra:
[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]
[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]
[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
To learn more on linear algebra: https://brainly.com/question/1952076
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