If $AB = 3 i - 4 j - k, BC = 4 i - j + 3 k$ are two sides of a $∆ ABC$ , then $∠ C =$

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$30^{\circ}$

$75^{\circ}$

$45^{\circ}$

$90^{\circ}$

answer is D.

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Detailed Solution

$AC = AB + BC = 7 i - 5 j + 2 k \cos c = \frac{BC . AC}{|BC| |AC|} = \frac{28 + 5 + 6}{\sqrt{16 + 1 + 9} \sqrt{49 + 25 + 4}} = \frac{39}{\sqrt{26} \sqrt{78}} = \sqrt{\frac{3}{2} \times \frac{3}{6}} = \frac{\sqrt{3}}{2} C = 30^{\circ}$

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