Answer:
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Step-by-step explanation:
The distance between two points A (2, 3, 4) and B (-5, 6, 7) can be calculated using the distance formula in three-dimensional space.
The distance formula is derived from the Pythagorean theorem and can be expressed as follows:
distance AB = √[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]
In this case, the coordinates of point A are (x1, y1, z1) = (2, 3, 4), and the coordinates of point B are (x2, y2, z2) = (-5, 6, 7).
Substituting the values into the formula, we have:
distance AB = √[(-5 - 2)^2 + (6 - 3)^2 + (7 - 4)^2]
Simplifying the equation:
distance AB = √[(-7)^2 + (3)^2 + (3)^2]
distance AB = √[49 + 9 + 9]
distance AB = √67
Hence, the distance between points A and B is √67 units.