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)?

1 Answer
Jan 26, 2017

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

parametric eqns:

x=3+2lambda

y=4+lambda

Explanation:

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