Question

Find the cartesian equation of the line passing through the points , A(2,−1,3) and B(4,2,1)is?

Answer 1

Answer:

The equation of line is :

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

Step-by-step explanation:

Given :

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

We know, equation of line passing through two given points is :

$\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}=\dfrac{z-z_1}{z_2-z_1}$

( Here two points are A $(x_1,y_1,z_1)$ and B $(x_2,y_2,z_2)$ )

Putting value of point A and B in above equation.

We get ,

$\dfrac{x-2}{4-2}=\dfrac{y+1}{2+1}=\dfrac{z-3}{1-3}\\\\\dfrac{x-2}{2}=\dfrac{y+1}{3}=\dfrac{z-3}{-2}$

The equation of line is :

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

Hence , this is the required solution.

Learn More :

Geometry

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Answer 2

The Cartesian equation of the line passing through the points , A(2,−1,3) and B(4,2,1) is $\frac{x-2}{2}=\frac{y+1}{2+1}=\frac{z-3}{-2}$.

To find : Cartesian equation.

Given :

Cartesian equation of the line passing through the points

A(2, -1, 3) and B(4, 2, 1)

Formula used :

Cartesian equation

Line passing through the points $(x_1,y_1, z_1) \ and \ (x_2, y_2, z_2)$.

$\frac{x-x_1}{x_2 - x_1}=\frac{y- y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$      

From the given data, there are two points.

A(2, -1, 3) and B(4, 2, 1) -----> ( 1 )

$(x_1,y_1, z_1)$ and $(x_2, y_2, z_2)$ -----> ( 2 )

Comparing ( 1 ) and ( 2 ), we get

$x_1$ = 2 ; $x_2$ = 4

$y_1$ = -1 ; $y_2$ = 2

$z_1$ = 3 ; $z_2$ = 1

Applying the values in the equation we get,

$\frac{x-x_1}{x_2 - x_1}=\frac{y- y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

$\frac{x-2}{4 - 2}=\frac{y- (-1)}{2-(-1)}=\frac{z-3}{1-3}$

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

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

Therefore, the Cartesian equation is $\frac{x-2}{2}=\frac{y+1}{2+1}=\frac{z-3}{-2}$.

To learn more...

1. Find the cartesian equation of the line passing through the points , A(2,−1,3) and B(4,2,1)

brainly.in/question/13656863

2. Find the Cartesian equation of the plane passing through points A (0,0,0) and B (3,−1,2) and parallel to the line  \frac{x-4}{1}=\frac{y+3}{-4}=\frac{z+1}{7}

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