What Are Orthogonal Vectors and When to Use Cross Product?

[Fatimah od]

Hi

I have a final exam after tomorrow, ,so I hope if anybody can help

1) How to find a unit vector that is orthogonal to both u=(1,1,0) and v=(-1,0,1) ?

2) How to determine whether the given planes are parallel :
3x_2y+z =6 and 2x_y+4z=0

I know how to determine whether the planes are perpendicular, it's to product their normals and get a zero. Is not?

3) when should I use the cross product?

Thanx you alot,

 

[JG89]

For 1) use the cross product. For 2), I haven't done planar algebra in a long time, but it would make sense to me that if two planes were parallel, then if n_1 and n_2 were the normals for the first and second plane, respectively, then n_1 would be a scalar multiple of n_2, i.e. n_1 = k*n_2 for some scalar k.

For 3), nobody can answer that. You're going to have to use the cross product and get a feel for it to determine whether a situation calls for it or not.

 

[SammyS]

Hi

I have a final exam after tomorrow, ,so I hope if anybody can help

1) How to find a unit vector that is orthogonal to both u=(1,1,0) and v=(-1,0,1) ?

2) How to determine whether the given planes are parallel :
3x_2y+z =6 and 2x_y+4z=0

I know how to determine whether the planes are perpendicular, it's to product their normals and get a zero. Is not?

3) when should I use the cross product?

Thanx you alot,

Hello Fatimah od . Welcome to PF.

According to the Forum Rules for Homework Help:

"NOTE: You MUST show that you have attempted to answer your question in order to receive help. You MUST make use of the homework template, which automatically appears when a new topic is created in the homework help forums.
...

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. "​

So you see, our hands are tied. We can't help until you show what you know about these questions.

 

[Fatimah od]

JG89

So thanx, , that is completely help