First, let's find the magnitudes of the given vectors:
(a) $|-9 \mathbf{i}+6 \mathbf{j}| = \sqrt{(-9)^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}$
(b) $|-3 \mathbf{i}+9 \mathbf{j}| = \sqrt{(-3)^2 + 9^2} = \sqrt{9 + 81} = \sqrt{90}$
(c) $|-3 \mathbf{i}-5 \mathbf{j}| =
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