Question

Taking A (vector) = (6.00i-8.00j) units, B (vector) =(-8.00i+3.00j) units, and C (vector) = (26.0i+19.0j) units, determine a and b such that aA+bB+C=0

Answer 1

Do you have any ideas about this?

You should start by writing the sum explicitly:
\[a\vec{A} + b\vec{B} + \vec{C} = a(6.00\hat{i} - 8.00\hat{j}) + b(-8.00\hat{i} + 3.00\hat{j}) + (26.0\hat{i} + 19.0\hat{j}).\]
If this vector is to be the zero vector \(\vec{0}\) what must happen to each of its components?