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  • Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio 2 : 3 externally.

1 (ii) Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, – 4, 6) in the ratio 2:3 externally. 

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The line segment joining the points A (-2, 3, 5) and B (1, -4, 6)

Let point P(x,y,z) be the point that  divides the line segment AB externally in the ratio 2:3.

Now, as we know by section formula , The coordinate of the point P, which divides line segment A(x_1,y_1,z_1) And B(x_2,y_2,z_2)  externally, in ratio m:n is 

\left (\frac{mx_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n},\frac{mz_2-nz_1}{m-n} \right )

Now the point that divides A (-2, 3, 5) and B (1, -4, 6) externally in ratio 2:3 is 

\left (\frac{2(1)-3(-2)}{2-3},\frac{2(-4)-3(3)}{2-3},\frac{2(6)-3(5)}{2-3} \right )=\left ( -8,17,3\right )

Hence, required point is: 

. ( -8,17,3)

Posted by

Pankaj Sanodiya

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