Calculus 3 problem: lines and planes in space

[dfcitykid]

Let u=<5,-2,3> and v=<-2,1,4>. Find the value of c which will force the vector w=<2c,3,c-1> to lie in the plane of u and v. I did the cross product of u and v, then i crossed u and w, then I equal the product of u and v with what I got for w. But for some reason when I try doing the triple scalar of u,v, and w; it does not give me zero which would prove that w is in the plane of u and v.

 

[Fredrik]

It will be much easier for us to help you if you post the calculation that got the wrong result. Here's a dot product symbol and a cross product symbol that you can copy and paste: · ×

 

[_N3WTON_]

Let u=<5,-2,3> and v=<-2,1,4>. Find the value of c which will force the vector w=<2c,3,c-1> to lie in the plane of u and v. I did the cross product of u and v, then i crossed u and w, then I equal the product of u and v with what I got for w. But for some reason when I try doing the triple scalar of u,v, and w; it does not give me zero which would prove that w is in the plane of u and v.

I think you may be doing the problem incorrectly. The scalar triple product formula is a • (b x c). So I do not believe you need to cross u and v and u and w and equate them. I'm not 100% certain though (I'm currently taking calc 3 myself) so perhaps someone can confirm or deny my suspicion.

 

[LCKurtz]

You could just write the equation$$
\vec w = a\vec u + b\vec v$$out and set the components equal. 3 equations in 3 unknowns.

Alternatively, and probably easier, just dot ##\vec w## with ##\vec u \times \vec v##, which is normal to the plane, and and set it equal to zero. Then you can just solve for ##c##.