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If the three different points P(3u², 2u³), Q(3v², 2v³), and R(3w², 2w³) lie on one straight line, then which relation must hold?
- uv + vw + wu = 0
- uv + vw + wu = 3
- uv + wu = 2
- uv + vw + wu = 1
Correct answer: uv + vw + wu = 0
Solution
The points P, Q, and R are collinear if the area of the triangle they form is zero, which leads to the condition that the determinant formed by their coordinates equals zero. This results in the relation uv + vw + wu = 0, indicating that the weighted sum of the products of the coordinates must balance out to maintain collinearity.
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