Question

Find the equation to the line passing through the point (1,-2,-3) and parallel to the line 2x+3y-3z+2=0=3x-4y+2z-4.

Answer 1

$\begin{array}{c}\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& -3\\ 3& -4& 2\end{array}\right|\\ =\hat{i}\left(6-12\right)-\hat{j}\left(4+9\right)+\hat{k}\left(-8-9\right)\\ =\left(-16\hat{i}-13\hat{j}-17\hat{k}\right)\\ so,equationatline:-\\ r=p+t.n\\ =\left(\hat{i}-2\hat{j}-3\hat{k}\right)+t\left(-6\hat{i}-13\hat{j}-17\hat{k}\right)\end{array}$