If $\mathrm{A}=(1,2,3), \mathrm{B}=(3,4,7)$ and $\mathrm{C}=(-3,-2,-5)$ are three points then the ratio in…

If $\mathrm{A}=(1,2,3), \mathrm{B}=(3,4,7)$ and $\mathrm{C}=(-3,-2,-5)$ are three points then the ratio in which the point C divides AB externally is
  1. $2: 3$
  2. $3: 2$
  3. $4: 3$
  4. $3: 4$

Solution

$\mathrm{A}=(1,2,3), \mathrm{B}=(3,4,7) \text { and } \mathrm{C}=(-3,-2,-5)$
Let ratio be $\mathrm{k}: 1$ $\mathrm{C}(-3,-2,-5)=\left(\frac{3 k-1}{k-1}, \frac{4 k-2}{k-1}, \frac{7 k-3}{k-1}\right)$
On comparing, $\frac{3 k-1}{k-1}=-3 \Rightarrow k=\frac{2}{3}$ $\therefore$ Required ratio $=2: 3$

Asked in: AP EAMCET 2024 (22 May Shift 2)

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