Find the Component of a Vector Perpendicular to a Plane | Magnitude 3

[Shay10825]

Hello. I need some help with the following problem:

Find the component of u if u is perpendicular to the plane x- 3y + 4z =0 and the magnitude of u is 3.

My work:

Some vector v is on the plane

v = 1i – 3j + 4k

so then the dot product of u and v = 0

Now I’m stuck and don’t know where to go from here.

The answer in the back of the book is: [3/sqrt 26]i - [9/sqrt 26]j + [12/sqrt 26]k

Any help would be greatly appreciated.

Thanks

 

[neurocomp2003]

do you know what th edefinition of a plane equation is? and have you seen this equation before N.P-N.P0=0 OR N.(P-P0)=0 or N.P+D=0

do you know what the number SQRT(26) stands for in your above question?
and do you know how to change the magnitude of a given vector?

 

[Shay10825]

do you know what th edefinition of a plane equation is? and have you seen this equation before N.P-N.P0=0 OR N.(P-P0)=0 or N.P+D=0

do you know what the number SQRT(26) stands for in your above question?
and do you know how to change the magnitude of a given vector?

yes I know the definition of a plane. Yes I have seen the equation of a plane before in the form a(x-x1) + b(y-y1) + c(z-z1) = 0.

Yes I know that the sqrt(26) in the answer is the magnitude of v (v = 1i – 3j + 4k ). And i think I know how to change the magnitude of a vector (if you mean change a vector into a unit vector, then yes).

I know the answer the book gave is v/(the magnitude of v). But why would you do that to get the "component of u if u is perpendicular to the plane x- 3y + 4z =0 and the magnitude of u is 3"

Thanks

 

[Shay10825]

is the vector v = 1i – 3j + 4k on the plane?

 

[Shay10825]

Ohhh. I see where you were going. Thanks. I see it not. I did not realize that the vector I found was perpendicular to the plane because of the definition of a plane. I assumed that the vector was on the plane.

Thanks