Question

For the following vectors, find 2u - 3(v - w): u = <5, - 1>, v = <-2, 1>, W = <-1,0>O <15, -5><13, 1>O <13, -5><7, 1>

Answer 1

As per given by the question,

There are given that,

`u=<5,\text{ -1>, v=<-2, 1>, w=<-1, 0>}`

Then find the value of;

`2u-3(v-w)`

Now,

If u=<5, -1>, then 2u is;

`\begin{gathered} 2u=2(5,\text{ -1)} \\ =(10,\text{ -2)} \end{gathered}`

If, v=<-2, 1>, and w=<-1, 0>, then 3(v-w) is;

`\begin{gathered} 3(v-w)=3((-2,\text{ 1)-(-1, 0)} \\ =3(-2+1,\text{ 1-0)} \\ =3(-1,\text{ 1)} \\ =(-3,\text{ 3)} \end{gathered}`

Now,

Put the value of 2u and 3(v-w) in given function 2u-3(v-w),

So,

`\begin{gathered} 2u-3(v-w)=(10,\text{ -2)-(-3, 3)} \\ =(10+3,\text{ -2-3)} \\ =(13,\text{ -5)} \end{gathered}`

So, the value of given function 2u-3(v-w) is <13, -5>.

Hence, the option C is correct.