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#