Find the equation of the line drawn through point (1, 0, 2) to meet the line `(x+1)/3=(y-2)/(-2)=(z1)/(-1)` at right angles.

Explanation

Given line at `overset(harr)(AB)-=(x+1)/(3)=(y-2)/(-2)=(z+1)/(-1)" "`(i)
Let `P-=(1, 0, 2)`
Any point on line (i) is `Q-=(3r-1, -2r+2, -r-1)`
Direction ratios of `PQ " are "3r-2, -2r+2, -r-3`
Direction ratios of line `AB" are "3, -2, -1`
`because" "PQbotAB`
`therefore" "3(3r-2)-2(-2r+2)-1(-r-3)=0`
or `" "14r=7 or r=(1)/(2)`
Therefore, direction ratio of PQ are `-(1)/(2), 1, -(7)/(2) or 1, -2, 7`
`" "`Equation of line `PQ-=(x-1)/(1)=(y)/(-2)=(z-2)/(7)`