Question

Find symmetric equations for the line that passes through the point (4, −2, 8) and is parallel to the vector −1, 3, −4 .

Answer 1

`(x-4)/(-1)=(y+2)/(3)=(z-8)/(-4)`

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 (
`x_1,y_1,z_1`) and parallel to vector <a,b,c> is given by

`(x-x_1)/(a)=(y-y_1)/(b)=(z-z_1)/(c)`

`x_1=4,y_1=-2,z_1=8` and <a,b,c>=<-1,3,-4>

Using the formula

The symmetric equation of the line

`(x-4)/(-1)=(y+2)/(3)=(z-8)/(-4)`

This is required symmetric equation of line.