how do you prove that two lines in 3D are coplanar? Apply that to Prove the following questionQuestion : Prove that the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 are coplanar.Solution: We know that lines \[\frac{x-x_1}{a_1}=\frac{y-y_1}{b_1}=\frac{z-z_1}{c_1}\ and\frac{x-x_2}{a_2}=\frac{y-y_2}{b_2}=\frac{z-z_2}{c_2}\] are coplanar if \[\left|\begin{matrix}x_2-x_1&y_2-y_1&z_2-z_1\\a_1&b_1&c_1\\a_2&b_2&c_2\\\end{matrix}\right|=0\] Therefore for…
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