Question

the Cartesian equation of the line passing through the points A(4,2,1)and B(2,-1,3)​

Answer 1

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$\Large\boxed{(x-x1)/(x2-x1)=(y-y1)/(y2-y1)=(z-z1)/(z2-z1)}$

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Answer 2

The equation of line is :

$\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-3}{-2}$.

Given :

Two points A(4,2,1) and B(2,-1,3).

We need to find the equation of line passing through them.

We know equation of line through point $\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$.

Putting points A and B in above equation we get :

$\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-3}{-2}$.

Hence , this is the required solution.

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Coordinate Geometry

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