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**[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?**