A force $$\(\mathbf{F}\)$$ is given by $$\(\mathbf{F}=(10 \mathbf{i}+\mathbf{j}) \mathrm{N}\)$$. (a) Find the exact value of the magnitude of $$\(\mathbf{F}\)$$. (2) (b) Find, in degrees, the size of the angle between the direction of $$\(\mathbf{F}\)$$ and the direction of the vector $$\((\mathbf{i}+\mathbf{j})\)$$. (4) The resultant of the force $$\(\mathbf{F}\)$$ and the force $$\((-15 \mathbf{i}+a \mathbf{j}) \mathrm{N}\)$$, where $$\(a\)$$ is a constant, is parallel to, but in the opposite direction to, the vector $$\((2 \mathbf{i}-3 \mathbf{j})\)$$. (c) Find the value of $$\(a\)$$. (5)

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