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 a lot,

 

[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 a lot,

Hello Fatimah od . Welcome to PF.

According to the Forum Rules for Homework Help:

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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