Understanding Direction Vectors in Vector Geometry

[kougou]

[equation for a line] help...

Homework Statement

so, as i am reading the textbook, it says, " given a point P it its evident geometrically that there is exactly one line through p which is parallel to a given non zero vector. This non zero vector is d (vector) is called a direction vector for the line if it's parallel to the line; that is, if d is parallel to AB for soe distinct points A and B on the line".

so confusion arises: I am not sure whether the direction vector d is on the on the line or not! you know, we could have any vector in the space, and as long as that vector is parallel to the line, then it's direction vectors... Am I missing something?

 

[2h2o]

A direction vector is exactly that: it signifies only direction. It says nothing about position or magnitude; hence it may be on the line, but not necessarily. But that's not terribly useful, just in of itself; so your textbook is probably just going to use it as a way to build up to describing vectors in component form (the i, j, k vectors are unit directional vectors.)

I know, my description is horribly convoluted. Sorry, it's a bit confusing at first, but keep working through it--keep reading! Pretty soon, you'll be more comfortable with vectors in component form than in magnitude-direction form. Or not (maybe it's just me, but I'm strange in that I <3 cross-products; unlike most of my classmates it seems.)