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 = 7

Answer 1

r=<1,0,9>+t<1,2,1>

and

x=1+t

y=2t

z=9+t

Explanation:

A vector perpendicular to the plane :

`ax+by+cz+d=0`

is given by (a,b,c)

So a vector perpendicular to given plane will have :

(1,2,1)

`The\ parametric\ equation\ of\ a\ line\ through\ (1,0,9)\ and\ parallel\ to\ vector\ (a,b,c) is\ given\ by:\\x=x_0+ta\\y=y_0+tb\\z=z_0+tb\\x=1+t(1)\\x=1+t\\y=0+t(2)\\y=2t\\z=9+t(1)\\z=9+t\\The\ vector\ form\ is:\\r=<1,0,9>+t<1,2,1>` ..