A particle of mass $$\(2 \mathrm{~kg}\)$$ is moving with velocity $$\((5 \mathbf{i}+3 \mathbf{j}) \mathrm{ms}^{-1}\)$$ when it receives an impulse $$\(\mathbf{I N}\)$$ s, such that $$\(\mathbf{I}=a \mathbf{i}+b \mathbf{j}\)$$ Immediately after receiving the impulse, the particle is moving with velocity $$\(\lambda(\mathbf{i}+\mathbf{j}) \mathrm{m} \mathrm{s}^{-1}\)$$, where $$\(\lambda\)$$ is a constant. Given that the magnitude of $$\(\mathbf{I}\)$$ is $$\(\sqrt{40}\)$$, find the two possible impulses. (5)

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