Question Number 98018 by hardylanes last updated on 11/Jun/20
$${the}\:{vector}\:{equations}\:{of}\:{two}\:{lines}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \:{are}\:{given}\:{by} \\ $$$${l}_{\mathrm{1}} :{r}=\mathrm{5}{i}−{j}+{k}+\lambda\left(−\mathrm{3}{i}+\mathrm{2}{j}\right) \\ $$$${l}_{\mathrm{2}} :{r}=\mathrm{2}{i}+\mathrm{3}{j}+\mathrm{2}{k}+\mu\left(\mathrm{2}{j}+{k}\right) \\ $$$${find} \\ $$$${thd}\:{position}\:{vdctor}\:{of}\:{intersection}\:{of}\:{thf}\:{linds}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \: \\ $$$${thd}\:{cartesian}\:{equatkon}\:{of}\:{the}\:{plane}\:\pi,\:{containing}\:{the}\:{lines}\:{l}_{\mathrm{1}\:} {and}\:{l}_{\mathrm{2}} \\ $$$${the}\:{sine}\:{of}\:{the}\:{anhle}\:{between}\:{the}\:{plane}\:\pi\:{and}\:{the}\:{line},\:{l}_{\mathrm{3}} :{r}={i}−\mathrm{5}{j}−\mathrm{2}{k}+{s}\left(\mathrm{2}{i}+\mathrm{2}{j}−{k}\right) \\ $$
Answered by Rio Michael last updated on 11/Jun/20