Math Is Fun Forum

EMPhillips1989

Member

Registered: 2008-01-21

Posts: 40

vector equations

does anyone know why the vector equations

and

both describe a straight line in the direction of c through the point d??

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: vector equations

well the first one is your normal equation for a straight line.

if you have r = ct. then from the origin (t = 0) you are moving along the vector 'c'. which gives a straight line. having the +d means you can move the position of the equation at t = 0. hence, moving the straight line through space.

do you mean dot/scalar or cross/vector product in the second one, if you mean dot/scalar product then the second equation however does not define a straight line in direction of c, through d. the second equation describes the line that passes through d, and is perpendicular to c, of which in 3 or more dimensions, there are an infinite amount.

if you do mean cross/vector product, then it is (although a bit lack) the equation of said line. |a×b| = |a||b|sinθ. so if |a×b| = 0, then the angle between them is 0 - they are parallel - i.e. (r-d) is parallel to c. so take any point. translate it by d, and it is paralell to c. i.e. in direction of c - it passes through d, because when r = d, you have 0×c = 0

Last edited by luca-deltodesco (2008-02-09 04:28:08)

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