Finding Normal Components of a Plane Perpendicular to a Line in 3-Space

[Aliboy]

Homework Statement

A plane is perpendicular to the line given by x=3+6t, Y=7+4t, and z=7-9t. What are the components of the normal to the plane

Homework Equations

The Attempt at a Solution

I don't understand what the question is asking me all I have figured out that the normal should be parallel to the perpendicular line, but I can't find the normal from the parametric.

 

[Dick]

Homework Statement

A plane is perpendicular to the line given by x=3+6t, Y=7+4t, and z=7-9t. What are the components of the normal to the plane

Homework Equations

The Attempt at a Solution

I don't understand what the question is asking me all I have figured out that the normal should be parallel to the perpendicular line, but I can't find the normal from the parametric.

You can find the tangent vector to the parametric, right? What is it? Then sure, that should be parallel to the normal. Do you want a unit normal vector?

 

[Aliboy]

The only thing I don't understand is finding the tangent vector, all my book and teacher have told me is how to find the vector orthogonal to the plane.

 

[Dick]

The only thing I don't understand is finding the tangent vector, all my book and teacher have told me is how to find the vector orthogonal to the plane.

The tangent vector to the parametric curve (x(t),y(t),z(t)) is the derivative with respect to t of that. It's (x'(t),y'(t),z'(t)). What is that?

 

[Aliboy]

So 6,4,-9?
So the answer would be <6,4,-9>

 

[Dick]

So 6,4,-9?
So the answer would be <6,4-9>

That's a normal vector to your plane alright. Any multiple of that is also a normal, yes? Do they want any specific one? That's why I asked if you want a 'unit normal'.

 

[Aliboy]

I guess that should do I just don't understand the conceptual behind it.

 

[Dick]

I guess that should do I just don't understand the conceptual behind it.

When you said, "I have figured out that the normal should be parallel to the perpendicular line" then that pretty much sums it up. Finding a vector tangent to the perpendicular line will then give you a normal. Just as you did.

 

[Aliboy]

Thank you very much it actually makes sense now.

 

[HallsofIvy]

Part of your problem is shown here:

The only thing I don't understand is finding the tangent vector, all my book and teacher have told me is how to find the vector orthogonal to the plane.

A plane doesn't have "the tangent vector". Every line in the plane gives a tangent vector. A plane is completely determined by a single point and a vector normal to the plane.