Question

Find the Parametric equation of the line, which passes through the points: a=(1,2,3), b=(2,0,-4)

Answer 1

Answer:

(x,y,z) = (1+s, 2-2s,3-7s)

Step-by-step explanation:

Given that a line in three dimension passes through two points a and b

We have equation of the line passing through two points

$(x_1,y_1,z_1) \\(x_2,y_2,z_2)$ is

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

Substitute for the two points and equate to s

$\frac{x-1}{2-1} =\frac{y-2}{0_2} =\frac{z-3}{-4-3}=s$

Simplify to write

$\frac{x-1}{1} =\frac{y-2}{-2} =\frac{z-3}{-7} =s\\x=1+s:  y= 2-2s:   z=3-7s$

Thus parametric form is

(x,y,z) = (1+s, 2-2s,3-7s)