Find the point where line which passes through point `(1,2,3)` and is paralle to line ` vec r= hat i+ hat j+2 hat k+lambda( hat i-2 hat j+3 hat k)` meets the xy-plane.

Explanation

Line is passing through the point (1, 2, 3) and parallel to the line `vecr=hati-hatj+2hatk+lamda(hati-2hatj+3hatk)` or parallel to the vector `hati-2hatj+3hatk`. Hence, equation of line is
`" "(x-1)/(1)=(y-2)/(-2)=(z-3)/(3)`
It meets `xy`-plane, where `z`=0
Then from the equation of line, we have
`" "(x-1)/(1)=(y-2)/(-2)=(0-3)/(3)`
`rArr" "x=0, y=4`.
Hence, line meets`xy`-plane at (0, 4, 0).