Question

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1, 0, 9) and perpendicular to the plane x 2y z

Answer 1

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  $(x_{0} ,y_{0}, z_{0} )$  and parallel to the vector  ⟨ a , b , c ⟩  is  

$x=x_{0} +ta\\y=y_{0} +tb\\z=z_{0} +tc$

so the parametric equation of our line is

$x=1+t\\y=2t\\z=9+t$

The vector form of the line is  

$r=+t$