Discussion
If a point P with x -coordinate 7 lies on the line joining the points A (1, 2, 3) and B (4, 6, 8) then the coordinates of the point P are
Answer: D
P is (7, 10, 13).
The direction from A(1, 2, 3) to B(4, 6, 8) is (3, 4, 5), so points of the line are \((1 + 3t, 2 + 4t, 3 + 5t)\). For x = 7, \(1 + 3t = 7\) gives t = 2:
\[ (1 + 6, 2 + 8, 3 + 10) = (7, 10, 13) \]
So P lies beyond B, with AP = 2AB. The options with -10 or -13 have the wrong signs, and (7, 10, 12) and (7, 10, 15) have the right y but a z that does not lie on the line.
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