class 12

Missing

JEE Advanced

Let \displaystyle\vec{{a}}={2}\hat{{i}}+\hat{{j}}-\hat{{k}}&\vec{{b}}=\hat{{i}}+{2}\hat{{j}}+\hat{{k}} be two vectors. Consider a vector $C=αa+βb,α,β∈R$. If the projection of $c$ on the vector $(a+b)$ is $32 $ then the minimum value of $(c−(a×b)).c$ equal to