Find the direction cosines of the lines, connected by the relations: `l+m+n=0` and `2l m+2ln-m n=0.`

Options

A. `(l_(1))/(l_(2))+(m_(1))/(m_(2))+(n_(1))/(n_(2))` is equal to `-3/2`
B. `l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2)` is equal to `-1/2`
C. `l_(1)+(m_(1)n_(1)+l_(2)m_(2)n_(2)` is equal to `-(sqrt(2))/(3sqrt(3))`
D. `(l_(1)+l_(2)(m_(1)+m_(2))(n_(1)+n_(2))` is equal to `1/(3sqrt(6))`

Answer

A, B, C, D

Explanation

By eliminating `n2 (l/m)^(2)=l/m-1=0`
`implies(l_(1))/(m_(1))=1, (l_(2))/(m_(2))=-1/2`
On solving we ger `(l_(1),m_(1),n_(1))=(1/(sqrt(6)),1/(sqrt(6)),-sqrt(2/3))` and `(l_(2),m_(2),n_(2))=(1/(sqrt(6))-sqrt(2/3),1/(sqrt(6)))`