The equation of the line through the point (0,1,2) and perpendicular to the line 2x−1=3y+1=−2z−1 is:
Solutions · 1
Official solution
\[{{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over { - 2}} = \lambda \]
Any point on this line \[(2\lambda + 1,3\lambda - 1, - 2\lambda + 1)\]
Direction ratio of given line (2,3,−2)
Direction ratio of line to be found \[(2\lambda + 1,3\lambda - 2, - 2\lambda - 1)\]
\[ \therefore \] \[{\overrightarrow d _1}\,.\,{\overrightarrow d _2} = 0\]
\[ \Rightarrow \] \[\lambda = 2/17\]
Direction ratio of line \[(21, - 28, - 21) \equiv (3, - 4, - 3) \equiv ( - 3,4,3)\]