Find the angle between the vectors a = (2, 2, -1) and b = (1, 3, 2). | Mathematics I 2079

Mathematics I20795 marksNumerical: angle between vectorsDot product and cross Product

Find the angle between the vectors $a = (2, 2, -1)$ and $b = (1, 3, 2)$ . [5]

Find the angle between the vectors $a = (2, 2, -1)$ and $b = (1, 3, 2)$. [5]

$\mathbf{a} = (2, 2, -1), \qquad \mathbf{b} = (1, 3, 2)$ Formula for the angle $\theta$ : $\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{a}\,\mathbf{b}}$ --- $\mathbf{a} \cdot \mathbf{b} = (2)(1) + (2)(3) + (-1)(2) = 2 + 6 - 2 = 6$ $$\mathbf{a} = \sqrt{2^2 + 2^2 + (-1)^2} = \sqrt{4...

$$\mathbf{a} = (2, 2, -1), \qquad \mathbf{b} = (1, 3, 2)$$ Formula for the angle $\theta$: $$\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{a},\mathbf{b}}$$ --- $$\mathbf{a} \cdot \mathbf{b} = (2)(1) + (2)(3) + (-1)(2) = 2 + 6 - 2 = 6$$ $$\mathbf{a} = \sqrt{2^2 + 2^2 + (-1)^2} = \sqrt{4...

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