Mathematics

Question : Find the equation of the plane through (1 2 3) parallel to the plane 4x+5y-3z=7 Solution : Let equation of the plane is ax+by+cz+d=0                                                                             (1) Since this plane…

Question: Find the equation of the plane containing two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 . Solution : First we shall find direction vector of the lines \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\] and \[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\] are \[\vec{d_1}=2\hat{i}+3\hat{j}+4\hat{k},\…

how do you prove that two lines in 3D are coplanar? Apply that to Prove the following question Question : 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:…