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3 cards from this section. Quick, good the night before a test.
Find the coordinates of the point that divides the segment joining (0, 0, 0) and (2, 2, 2) in the ratio 1:2.
Apply the section formula using the given coordinates.
What is the ratio for a point that equally divides the segment between (3, 3, 3) and (4, 4, 4)?
Think about equal division.
What does the section formula in three dimensions calculate?
Think about dividing segments in geometry.
The coordinates (5, 6, 7) divide the segment from (2, 3, 4) to (8, 9, 10) in what ratio?
Use the section formula to relate coordinates to ratio.
Consider points A(3, 2, 1) and B(7, 8, 5), a point divides the line segment AB externally in the ratio 4:3. Calculate the coordinates of the dividing point.
Refer to the section formula that accounts for external division.
Two points P(-5, -2, -3) and Q(5, 3, 7) create a segment divided by a point R in ratio 2:-1. Find the coordinates of point R.
The formula needs adjusting for negative ratios in external division.
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