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

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Answer 1 · 2017-02-08T23:38:58

$a= <-22,29>$

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

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