Mathematics - Vector Question with Solution | TestHub

Let$\overrightarrow{a}=\hat{i}+5\hat{j}+\alpha \hat{k}, \overrightarrow{b}=\hat{i}+3\hat{j}+\beta \hat{k}$and$\overrightarrow{c}=-\hat{i}+2\hat{j}-3\hat{k}$be three vectors such that,$|\overrightarrow{b}\times \overrightarrow{c}|=5\sqrt{3}$and$\overrightarrow{a}$is perpendicular to$\overrightarrow{b}.$Then the greatest amongst the values of$|\overrightarrow{a}{|}^2$is ________.