Using section formula, show that the points A(2, -3, 4)b(-1, 2, 1… - Vidyadip

Question

Using section formula, show that the points A(2, -3, 4)b(-1, 2, 1) and $C\left( {0,\frac{1}{3},2} \right)$ are collinear.

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Answer

Let the points b(-1, 2, 1) divides the join of A(2, -3, 4) and $C\left( {0,\frac{1}{3},2} \right)$ in the ratio k : 1 internally.
Then coordinates of B are $\left( {\frac{2}{{k + 1}},\;\frac{{\frac{1}{3}k - 3}}{{k + 1}},\;\frac{{2k + 4}}{{k + 1}}} \right)$
Now, $\frac{2}{{k + 1}} = - 1 \Rightarrow 2 = - k - 1 \Rightarrow k = - 3$
Thus the point B divides the join of A and C in the ratio -3:1 so points A, B, C are collinear.

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