Question

Find the equation of the straight line joining the points (2,5,8) and (-1,6,3)​

Answer 1

Equation of straight line is $\bf \frac{x - 2 }{ 3} = \frac{5 - y }{ 1} = \frac{z - 8 }{ 5}$

Given:

• Two points.
• (2,5,8) and (-1,6,3).

To find:

• Find the equation of the straight line joining the points.

Solution:

Formula to be used:

Equation of line passing through two points $(x_1, \: y_1, \: z_1)$ and $(x_2, \: y_2, \: z_2)$

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

Step 1:

Write the coordinates.

Let $(x_1 ,\: y_1, \: z_1) = (2,5,8)$

and

$(x_2, \: y_2, \: z_2) = ( - 1,6,3)$

Step 2:

Find the equation of straight line.

Put the coordinates in the equation,

$\frac{x - 2 }{ - 1 - 2} = \frac{y - 5 }{ 6 - 5} = \frac{z - 8 }{ 3 - 8}$

or

$\frac{x - 2 }{ - 3} = \frac{y - 5 }{ 1} = \frac{z - 8 }{ - 5}$

or

$\frac{x - 2 }{ 3} = \frac{y - 5 }{ - 1} = \frac{z - 8 }{ 5}$

or

$\frac{x - 2 }{ 3} = \frac{5 - y }{ 1} = \frac{z - 8 }{ 5}$

Thus,

Equation of straight line is $\bf \frac{x - 2 }{ 3} = \frac{5 - y }{ 1} = \frac{z - 8 }{ 5}$

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