transform.tex
3759b7e2ddc5runner

transform.tex
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			\documentclass[12pt]{article}

			\usepackage{amsmath}

			\begin{document}

			\begin{eqnarray*}
			\begin{pmatrix}
			\mathbf{a} &
			\mathbf{b} &
			\mathbf{c}
			\end{pmatrix}
			& = &
			\begin{pmatrix}
			a_x & b_x & c_x \\
			0 & b_y & c_y \\
			0 & 0 & c_z \\
			\end{pmatrix} \\
			a_x &=& A \\
			b_x &=& \mathbf{B} \cdot \mathbf{\hat{A}} \quad = \quad B \cos{\gamma} \\
			b_y &=& \|\mathbf{\hat{A}} \times \mathbf{B}\| \quad = \quad B \sin{\gamma} \quad = \quad \sqrt{B^2 - {b_x}^2} \\
			c_x &=& \mathbf{C} \cdot \mathbf{\hat{A}} \quad = \quad C \cos{\beta} \\
			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} \\
			c_z &=& \|\mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})}\|\quad = \quad \sqrt{C^2 - {c_x}^2 - {c_y}^2} \\
			\end{eqnarray*}

			\end{document}