Saved Bookmarks
| 1. |
Showthat thelines (x-1)/(2)=(y+1)/(3) "and" (x+1)/(5)=(y-2)/(2),z=2 do notintersect each other . |
|
Answer» <P> SOLUTION :Theequationsof the givenlines are`(x-1)/(2)=(y+1)/(3)=(z-0)/(1)=lambda`(say) `(x+1)/(5)=(y-2)/(1)=(z-2)/(0)=mu`(say) Anypoint onthe LINES(i) is`P(2lambda +1, 3lambda -1, lambda)` Any POINTON the line (ii) is`Q (5mu-1,mu+2,2)` If THELINES (i)and (ii) intersectthen Pand Qmustcoincide forsomeparticularvalues of `lambda " and' mu` This gives `2lambda+1 =5mu -1, 3lambda -1=mu+2 " and"lambda=2` `rArr {underset(lambda=-3)underset(3lambda -mu=3)(2lambda -5mu =-2)` Putting`lambda=2` in (iv)we get `mu =3` Clearly`lambda =2 " and" mu ` =3do not satisfy (ii) Hencethe givenlinesdo notintersecteach other . |
|