Question

algebraic vectors questions:
find the ordered pair to represent t in each equations if u(which has a line above the letter) = -i +4j and V(which has a line above it )=<3, -2>

1) t=u+v
2)t=4u -6v
3)t=1/2u+v
4)t=8u

please help me solve these !

Answer 1

Are you familiar with both forms that a vector can be written in?
So let's use vector u as an example:

Unit Vector Notation:\[\Large\rm \vec u=-\hat{i}+4\hat{j}\]
We can write the same vector in Component Form:
\[\Large\rm \vec u=<-1,4>\]

Understand that those mean the same thing?

Answer 2

\[\Large\rm \vec u=<-1,4>\]\[\Large\rm \vec v=<3,-2>\]
\[\Large\rm \vec t=\vec u+\vec v\]\[\Large\rm \vec t=<-1,4>+<3,-2>\]\[\Large\rm \vec t=<-1+3,~-2+4>\]You just add the corresponding components together.

Answer 3

For 2)\[\Large\rm \vec t=4\vec u-6\vec v\]\[\Large\rm \vec t=4<-1,4>-6<3,-2>\]Let's write our subtraction as addition, and give the negative to the 6.\[\Large\rm \vec t=4<-1,4>+(-6)<3,-2>\]Before we can add corresponding components,
we have to distribute the 4 to each component of the first vector,
and then do the same with the -6 and the second vector.\[\Large\rm \vec t=<-4,16>+(-6)<3,-2>\]\[\Large\rm \vec t=<-4,16>+<-18,12>\]Then as before, add :)\[\Large\rm \vec t=<-4+(-18),~16+12>\]