Answer:
the parameter equation of given line is
x= 1+t
y=0+ 2t
z= 9+t
( note: in plane no signs given so we assume + so x+2y+z)
Step-by-step explanation:
A vector perpendicular to the plane a x + b y + c z + d = 0 is given by ⟨ a , b , c ⟩
So a vector perpendicular to the plane x +2 y + z − = 0 is ⟨ 1 , 2 , 1 ⟩
The parametric equation of a line through [tex](x_{0} ,y_{0}, z_{0} )[/tex] and parallel to the vector ⟨ a , b , c ⟩ is
[tex]x=x_{0} +ta\\y=y_{0} +tb\\z=z_{0} +tc[/tex]
so the parametric equation of our line is
[tex]x=1+t\\y=2t\\z=9+t[/tex]
The vector form of the line is
[tex]r=<1,0,9>+t<1,2,1>[/tex]
