How do you find the vector equation and the parametric equations of the line that passes through the points A (3, 4) and B (5, 5)?

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Answer 1 · 2017-01-26T17:41:25

vector eqn: $vecr=((3),(4))+lambda((2),(1))$

parametric eqns:

$x=3+2lambda$

$y=4+lambda$

assuming we are working in 2D only

vector eqn of line : $vecr=veca+lambdavecd$

$vecr=$ general point on the line#

$veca=$ known point on the line#

$vecd=$ direction of line

$lambda=$ scalar

$vecd=vec(AB)$

$vec(AB)=vec(AO)+vec(OB)$

$vec(AB)=-vec(OA)+vec(OB)$

$vec(OA)=((3),(4)); vec(OB)=((5),(5))$

$vec(AB)=vecd==-((3),(4))+((5),(5))=((2),(1))$

we can use either $vec(OA),$ or $vec(OB)$ for $veca$

$vecr=((3),(4))+lambda((2),(1))$

for the parametric eqns
let $vecr=((x),(y))$

so $((x),(y))=((3),(4))+lambda((2),(1))$

$x=3+2lambda$

$y=4+lambda$