Question

r(t)= (1-t)<-2,-1> + t<1,2>

I don't know how to get to the answer which I know is this.

=<-2+3t, -1+3t>

This is parameterization for integral of a line segment and this part is holding me up. This is the example I could find but I'm not sure where they got the vector.

Answer 1

\[r \left( t \right)=(1-t)<-2,-1>+t<1,2>=(1-t)(-2 i-1 j)+t(1 i+2 j)\]
\[=-2 i-1j+2ti+t j+t i+2 t j=(-2+2 t+t) i+(-1+t+2 t) j=(-2+3 t)i+(-1+3t) j\]
=<-2+3t,-1+3t>

Answer 2

Well, I obviously need a break today. Thanks! Very helpful.

Answer 3

yw