Expert: Paul Klarreich - 3/25/2006

Question
Hi,

The vector equation r=a+km has r parallel to km
where k is a parameter of any variable, and a and m is a position vector. r pass a point in a.

I don't see how they are parallel, if they are then a will be = zero so that the line km and r
are parallel but that's meaningless as they collapse to singularity.

please help.

Answer
Hi, Kenji,

You wrote:
Subject:  vector equation
Question:  Hi,

The vector equation r=a+km has r parallel to km
where k is a parameter of any variable, and a and m is a position vector. r pass a point in a.

I don't see how they are parallel, if they are then a will be = zero so that the line km and r
are parallel but that's meaningless as they collapse to singularity.

please help.
-----------------------
If  R = A + kM   (using CAPITALS for vector quantities and lower-case for scalars)

then  R || M  (using || to mean 'parallel')   implies that:

R || kM  for any k.  

And therefore  R - kM  is parallel to M.

Since A = R - kM,  it must be that  A is also || R.  So A does not have to be zero, just parallel to M.

Does this help?