Question

Find the equation of the line that forms the intersection of the two planes x + y = 6 and 3y + z = 4. Write your answer in the form x(t) = x0 + at, y(t) = y0 + bt, z (t) = z0 + ct

Answer 1

x + y = 6              ------ (1)

3y + z = 4.           ------ (2)

Calculate z interms of y,

From the equation (2)

3y + z = 4. 

z=4-3y

Calculate z interms of x,

Multiply the equation (1) with 3

3x + 3y = 18      ------ (3)

Subtract equation (3) from equation (2).

z-3x=-14

z=3x-14 

--------------------------------

Hence the symmertric equation is

4-3y=3x-14 =z

 

Set symmetric into t

z=t

3x-14=t -----> x=(14+t)/3

4-3y=t -----> y=(4-t)/3