Final answer:
The distance between points in three-dimensional space can be calculated using the distance formula. Without the correct coordinates for point B, we cannot calculate the distance between B and G. Instead, we calculated the distance between points A and G, which is 13 units.
Step-by-step explanation:
The question involves the calculation of distance between two points in three-dimensional space. This is a fundamental concept in mathematics, specifically in geometry and vector analysis. Unfortunately, the distance between points B and G cannot be calculated because the coordinates for point B are not provided. Only the coordinates for points A (12,4,0) and G (0,0,3) are given. Assuming this is a typographical error, and you meant to find the distance between points A and G, one can use the distance formula for three-dimensional space as follows:
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- (Ax, Ay, Az) = (x2 - x1, y2 - y1, z2 - z1)
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- Distance = √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²]
For points A (12, 4, 0) and G (0, 0, 3), we substitute in the formula:
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- (Ax, Ay, Az) = (0 - 12, 0 - 4, 3 - 0) = (-12, -4, 3)
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- Distance = √[(-12)² + (-4)² + (3)²] = √[144 + 16 + 9] = √[169]
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- Distance = 13 units
The distance between points A and G is 13 units. However, please provide the correct coordinates for point B if the calculation is indeed for points B and G.