Find the point of intersection of line passing through `(0,0,1)` and the intersection lines `x+2y+z=1,-x+y-2za n dx+y=2,x+z=2` with the `x y` plane.

Options

A. `((5)/(3),-(1)/(3),0)`
B. (1,1,0)
C. `((2)/(3),-(1)/(3),0)`
D. `(-(5)/(3),(1)/(3),0)`

Answer

a

Explanation

Equation of line.
`x+2y+z-1+lamda(-x+y-2z-2)=0" "(i)`
`x+y-2+mu(x+z-2)=0" "(ii)` `(0,0,1)"lies on it"implieslamda=0,mu=-2`
For point of intersection, z=0 and slove (i) and (ii).