If \overrightarrow{a} and \overrightarrow{b} are two vectors such that |\overrightarrow{a}+\overrightarrow{b}|=5 \sqrt{2} and \overrightarrow{a} \times(4 \hat{i}+\lambda \hat{j}+2 \hat{k})=(4 \hat{i}+\lambda \hat{j}+2 \hat{k}) \times \overrightarrow{b} and (\overrightarrow{a}+\overrightarrow{b}) \cdot(-3 \hat{i}+2 \hat{j}+\lambda \hat{k})=10 then

Sum of values of \lambda=\frac{48}{7}

Product of value of \lambda=\frac{84}{7}