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>#