Let \(L\) be the line of intersection of planes \(\vec{r} \cdot(\hat{i}-\hat{j}+2 \hat{k})=2\) and \(\vec{r} \cdot(2 \ha…

Let \(L\) be the line of intersection of planes \(\vec{r} \cdot(\hat{i}-\hat{j}+2 \hat{k})=2\) and \(\vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})=2\). If \(P(\alpha, \beta, \lambda)\) is the foot of perpendicular on \(L\) from the point \((1,2,0)\), then the value of \(35(\alpha+\beta+\lambda)\) is equal to:

[JEE Main 2021, 22 Jul (Shift 2)]