Find the coordinates of the point that divides the join of

Question:

Find the coordinates of the point that divides the join of A(-2, 4, 7) and B(3, - 5, 8) extremally in the ratio 2 : 1.

Solution:

The coordinates of point $R$ that divides the line segment joining points $P\left(x_{1}\right.$, $\left.\mathrm{y}_{1}, \mathrm{z} 1\right)$

and $Q\left(x_{2}, y_{2}, z_{2}\right)$ externally in the ratio $m: n$ are

$\left(\frac{m x_{2}-n x_{1}}{m-n}, \frac{m y_{2}-n y_{1}}{m-n}, \frac{m z_{2}-n z_{1}}{m-n}\right)$

Point $A(-2,4,7)$ and $B(3,-5,8), m$ and $n$ are 2 and 1 respectively.

Using the above formula, we get,

$\left(\frac{2 \times 3-1 \times-2}{2-1}, \frac{2 \times-5-1 \times 4}{2-1}, \frac{2 \times 8-1 \times 7}{2-1}\right)$

$=(8,-14,9)$, is the point that divides the two point $A$ and $B$ externally in the ratio $2: 1$.

 

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