Vector perpendicular to the plane

[xstetsonx]

For what value of a is the vector v=(-2,1,a) perpendicular to the plane z=6x-3y+4?

i looked the book and my teacher's solution they are different so i just want to make sure i did this right...


Vector v is perpendicular to the plane if it is parallel to the plane’s normal vector. A vector which is normal (= perpendicular) to the plane is n=(6,-3, 4) Hence, v parallel n if their coordinates are proportional, i.e. −2/6=1/3=a/4, therefore a=4/3



can someone correct me if i am wrong?PLZ

 

[radou]

You got one component of the normal vector wrong.

 

[xstetsonx]

how? z=6x-3y+4 don't u just take the coefficient and that is your normal vector?

 

[Gigasoft]

Do you see a 4z in your equation?

 

[xstetsonx]

aw crap so is it -1 then?

 

[xstetsonx]

since i have two vectors why can't i do Vector1 . Vector2=0?
since the dot product says a.b=0 is perpendicular to each other?