[ |\mathbfA| = \sqrt2^2 + 4^2 + (-3)^2 = \sqrt4 + 16 + 9 = \sqrt29 \approx 5.385 ] [ |\mathbfB| = \sqrt1^2 + (-1)^2 + 2^2 = \sqrt1 + 1 + 4 = \sqrt6 \approx 2.449 ] [ \cos \theta = \frac\mathbfA \cdot \mathbfB = \frac-85.385 \times 2.449 \approx \frac-813.19 \approx -0.6065 ] [ \theta = \cos^-1(-0.6065) \approx 127.3^\circ ] Smaller angle = ( 127.3^\circ ) (since >90°, the acute angle would be ( 180 - 127.3 = 52.7^\circ ) — but problem asks for smaller between them; by definition in vector algebra, it’s ≤180°, so 127.3° is correct).
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