forked from lijiext/lammps
28 lines
827 B
TeX
28 lines
827 B
TeX
\documentclass[12pt]{article}
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\usepackage{amsmath}
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\begin{document}
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\begin{eqnarray*}
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\begin{pmatrix}
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\mathbf{a} &
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\mathbf{b} &
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\mathbf{c}
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\end{pmatrix}
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& = &
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\begin{pmatrix}
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a_x & b_x & c_x \\
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0 & b_y & c_y \\
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0 & 0 & c_z \\
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\end{pmatrix} \\
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a_x &=& A \\
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b_x &=& \mathbf{B} \cdot \mathbf{\hat{A}} \quad = \quad B \cos{\gamma} \\
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b_y &=& |\mathbf{\hat{A}} \times \mathbf{B}| \quad = \quad B \sin{\gamma} \quad = \quad \sqrt{B^2 - {b_x}^2} \\
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c_x &=& \mathbf{C} \cdot \mathbf{\hat{A}} \quad = \quad C \cos{\beta} \\
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c_y &=& \mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})} \times \mathbf{\hat{A}} \quad = \quad \frac{\mathbf{B} \cdot \mathbf{C} - b_x c_x}{b_y} \\
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c_z &=& |\mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})}|\quad = \quad \sqrt{C^2 - {c_x}^2 - {c_y}^2} \\
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\end{eqnarray*}
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\end{document}
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