equation of a line

[earless]

Find the equation of a plane passing thru the origin parallel to the vectors A=3i+j-2k and B=i-j+5k.

I dont know how to start, help!!

 

[pka]

The normal vector of the plane will be AxB.

 

[earless]

ok i got the answer but cant see why it is.If the two vectors are parallel to the plane then they themselves are parallel arent they?Can vectors be skew like lines?Dont they have to lie on the same plane inorder to take the cross product?

 

[pka]

If the two vectors are parallel to the plane then they themselves are parallel arent they?

Absolutely NOT.
Just make a “victory V” with your first two index fingers. Hold them parallel to the tabletop. Do you see that two non-parallel vectors that are each parallel to that plane?

Can vectors be skew like lines? Don’t they have to lie on the same plane in order to take the cross product?

Vectors are not fixed objects. A vector is really an equivalence class of objects defined by direction and length. Now that may be too abstract for you. But in fact that is the exact mathematical meaning of vectors.

Now if you still have the V made with two index fingers, use a finger on the other hand to point in a perpendicular way to the ‘lap’ of the V. That will represent the cross product.

Does that help you?

 

[earless]

I now see how two vectrs musnt be parallel themselves to be parallel to a plane.So you can take the cross product of two vectors A and B parallel to a plane and you can move the cross product AxB and make it the normal vector of the plane.Is that correct?