Mathematics - Vector Question with Solution | TestHub

Let$\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}$and$\overrightarrow{c}=\hat{j}-\hat{k}$be three vectors such that$\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}$and$\overrightarrow{a}·\overrightarrow{b}=1.$If the length of projection vector of the vector$\overrightarrow{b}$on the vector$\overrightarrow{a}\times \overrightarrow{c}$is$l,$then the value of$3l^2$is equal to _____.