If A=6i-8j,B=-8i+3j and C=26i+19j,find A and B,aA+bB+C=0

Answer 1

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Answer 2

aA+bB+C = a(6i-8j) + b(-8i+3j) + 26i+19j
So, that means you need to solve
6a-8b+26 = 0
-8a+3b+19 = 0
Now finish it off

Answer 3

Re_write the unit vectors in terms of column vectors, i.e,
6i-8j= (6 -8)
-8i+3j= (-8 3)
26i+19j= (26 19)
aA+bB+C=0
a(6 -8)+b(-8 3) +(26 19)=0
(6a -8a)+ (-8b 3b) +(26 19)=0

6a-8b+26=0
-8a+3b+19=0

6a-8b=-26....eqn(i)
-8a+3b=-19 ....eqn(ii)
solve using elimination method by multiplying eqn(i) by 4 and eqn(ii) by 3

24a-32b=-104
-24a+9b=-57

-23b=-161
b=7
substitute b=7 in eqn(i)
6a-8(7)=-26
6a-56=-26
6a=-26+56
6a=30
a=5
therefore, a=5 and b=7