Question

Given vectors a= (1, - 4) and b = (2, 5), find –2a+5b.Write your answer in component form.- 2a + 5b =?

Answer 1

We are given the following two vectors

`\begin{gathered} a=<1,-4> \\ b=<2,5> \end{gathered}`

We are asked to find the following

`-2a+5b`

First, multiply the vector a with the scaler -2 to get -2a

`\begin{gathered} -2a=<-2\cdot_{}1,-2\cdot-4> \\ -2a=<-2,8> \end{gathered}`

Now, multiply the vector b with the scaler 5 to get 5b

`\begin{gathered} 5b=<5\cdot2,5\cdot5> \\ 5b=<10,25> \end{gathered}`

Finally, add -2a and 5b to get -2a+5b

`\begin{gathered} -2a+5b=<-2,8>+<10,25> \\ -2a+5b=<-2+10,8+25> \\ -2a+5b=<8,33> \end{gathered}`

Therefore, the resultant vector in component form is

`-2a+5b=<8,33>`