How to turn these symmetric equations into the general form?

[Regtic]

I was solving this problem

and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in the general format.

How do I turn this into the general format to check my answer? It should be 2X +Y +4Z -7 = 0

Whenever I try i just get two equations that don't mix to give me x y and z in one equation but it should be right.

 

[Dick]

I was solving this problem View attachment 76531

and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' and took their cross product so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in the general format. View attachment 76532

How do I turn this into the general format to check my answer? It should be 2X +Y +4Z -7 = 0

Whenever I try i just get two equations that don't mix to give me x y and z in one equation but it should be right.

That's not the equation of a plane. It's the equation of a line. You might want to try the long way.

 

[Regtic]

Why can't you do it my way? I know it works, I've done it on other problems. My teacher's done it like that before too.

 

[Dick]

Why can't you do it my way? I know it works, I've done it on other problems. My teacher's done it like that before too.

I don't know what you are doing. Can you show us?

 

[Regtic]

Redid it to make it a bit clearer

 

[Mark44]

I'm with Dick here. The symmetric equations you show in post #1 are for a line, not a plane.

 

[Mark44]

In your 2nd attachment, under "Normal Plane" you have (12, -16, -2)t (1, 1, 1). That can't be the equation of a plane, because (1) it's not an equation, and (2) there should be two parameters, not just one, in the parametric form of the equation of a plane.

 

[Regtic]

In your 2nd attachment, under "Normal Plane" you have (12, -16, -2)t (1, 1, 1). That can't be the equation of a plane, because (1) it's not an equation, and (2) there should be two parameters, not just one, in the parametric form of the equation of a plane.

Ooo right. Damn, I forgot a lot from linear. Literally not a plane with only 1 parameter. Ok thanks