The following three equations define three planes:[br][math] \epsilon_{1}: a_{1} \cdot x + b_{1} \cdot y + c_{1} \cdot z = d_{1} [/math][br][math] \epsilon_{1}: a_{2} \cdot x + b_{2} \cdot y + c_{2} \cdot z = d_{2} [/math][br][math] \epsilon_{1}: a_{3} \cdot x + b_{3} \cdot y + c_{3} \cdot z = d_{3} [/math][br][br][br][b]Exercise[/b][br]a) Vary the sliders for the coefficient of the equations and watch the consequences.[br]b) Adjust the sliders for the coefficients so that[br][list][br][*] two planes are parallel,[br][*] three planes are parallel,[br][*] all three planes form a cluster of planes intersecting in one common line.[br][/list]