If A = (6i-8j) units, B = (-8i-3j) units, and C = (26i-19j) units, determine a and b

such that aA + bB + C = 0

given equation

aA + bB + C = 0

Putting the given values

a (6i-8j) + b (-8i-3j) + (26i-19j) = 0

i (6a - 8b) - j (8a + 3 b) = - 26 i + 19 j

comparing the coefficients of i and j

6a - 8b = - 26

8a + 3b = - 19.

multiplying first equation by 4 and second equation by 3

24a - 32 b = - 104

24a + 9b = - 57

9b + 32b = - 57 + 104

41 b = 47

b = 1.41

6 a - 8 x 1.41 = - 26

6a = - 14.72

a = - 2.45