Equation of a line in the plane π≡2x−y+z−4=0 which is perpendicular to the line whose equation is x−21=y−2−1=z−3−2  and which passes through the point of intersection of l and π is

Let direction ratios of the line be (a, b, c ,) then  2a-b+c=0  and a−b−2c=0, i.e., a3=b5=c−1Therefore, direction ratios of the line are (3, 5, - 1).Any point on the given line is (2+λ,2−λ,3−2λ) it lies on the given plane π if 2(2+λ)−(2−λ)+(3−2λ)=4or  4+2λ−2+λ+3−2λ=4 or λ=−1Therefore, the point of intersection of the line and the plane is (1, 3, 5).Therefore, equation of the required line is x−13=y−35=z−5−1