The Cartesian equation of the plane r→=(1+λ−μ)i^+(2−λ)j^+(3−2λ+2μ)k^ is

Given plane isr→=(1+λ−μ)i^+(2−λ)j^+(3−2λ+2μ)k^=(i^+2j^+3k^)+λ(i^−j^−2k^)+μ(−i^+2k^)which is a plane passing through  a→=i^+2j^+3k^and parallel to the vectors b→=i^−j^−2k^  and c→=−i^+2k^Therefore, it is perpendicular to the vectorn→=b→×c→=−2i^−k^Hence, equation of plane is - 2(x - 1) + (0)(y - 2)(z-3) = 0  or 2x+z = 5