Answer:
[tex]\frac{x-4}{-1}=\frac{y+2}{3}=\frac{z-8}{-4}[/tex]
Step-by-step explanation:
We are given that a point (4,-2,8)
Vector=<-1,3,-4>
We have to find the symmetric equation of line that passes through the point(4,-2,8) and parallel to given vector.
We know that the equation of line passing through the point ([tex]x_1,y_1,z_1[/tex]) and parallel to vector <a,b,c> is given by
[tex]\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}[/tex]
[tex]x_1=4,y_1=-2,z_1=8[/tex] and <a,b,c>=<-1,3,-4>
Using the formula
The symmetric equation of the line
[tex]\frac{x-4}{-1}=\frac{y+2}{3}=\frac{z-8}{-4}[/tex]
This is required symmetric equation of line.
