In three dimesnion, equation of a Line is determined using a fixed point on the line and any arbitrary point on the line and position vectors of these two points be r0 and r, then the equation of line is given by r-r0=S (by triangle law of addition), and this S is written as scalar times a vector which is parallel to it( let it be tV) (and I know if two vectors are parallel we can represent one vector as scalar times of another vector) and get the equation of Line r=r0=tV(adsbygoogle = window.adsbygoogle || []).push({});

But what is that S vector and to find the direction of S vector why do we need a new vector( let it be V) which is parallel to this S vector? and how do we know this new vector V is parallel to S vector?

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# Why the vector equation of Line in threedimension is defined that way?

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