Question

How do you find a=-b+4c given b=<6,3> and c=<-4,8>?

Answer 1

`a= <-22,29>`

Explanation:

If

`b= <6,3>`

`c=<-4,8>`

and

`a=-b+4c`

`<=>` substitute in

`a = (-1)<6,3>+4<-4,8>`

Since if you take a scalar `c` and multiply it by a vector `< a,b>` you get `c< a,b> = < ca, cb>` then we can multiply and get

`a = <-6,-3>+<-16,32>`

and since the addition of two vectors `a` and `b` makes a vector `a+b`

`a+b = < x_a+x_b,y_a+y_b>`

we can add the vectors algebraically

`a= <(-6-16),(-3+32)> = <-22,29>`