MHB *IBV5 The vectors u, v are given by u = 3i + 5j, v = i – 2j

[karush]

The vectors $u, v$ are given by $u = 3i + 5j, v = i – 2j$
Find scalars $a, b$ such that $a(u + v) = 8i + (b – 2)j$

$(u+v)=4i+3j$
in order to get the $8i$ let $a=2$
then $2(4i+3j)=8i+6j$
in order to get $6j$ let $b=8$ then $(8-2)j=6j$
so $a=2$ and $b=8$

I am not sure of the precise definition of what scalar means here...at least with vectors

 

[tkhunny]

vectors u,v are given by u=3i+5j,v=i–2j
Find scalars a,b such that a(u+v)=8i+(b–2)j

u + v = <4,3>

Then <4a,3a> = <8,(b-2)>

4a = 8

3a = b-2

 

[eddybob123]

I am not sure of the precise definition of what scalar means here...at least with vectors

The definition is the same with everything; basically a number. Whether it's restricted to real or complex numbers is usually clear from context.

 

[karush]

vectors u,v are given by u=3i+5j,v=i–2j
Find scalars a,b such that a(u+v)=8i+(b–2)j

u + v = <4,3>

Then <4a,3a> = <8,(b-2)>

4a = 8

3a = b-2

yes, that looks like a much better way to solve it. especially if it gets a lot more complicated.