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Mountainside Monitoring

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3 CO₂ monitors K, L and M are placed on a mountain side

The vector \(\overrightarrow{\text{KL}} = 3\mathbf{i -}6\mathbf{k}\) and \(\overrightarrow{\text{LM}} = 2\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}\), relative to a fixed origin.

Show that \(\angle KLM = 66.4°\) to one decimal place

[7 marks]

Hence find \(\angle LKM\) and \(\angle LMK\)

[3 marks]

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