Let a = i + j +2 k and b =- i +2 j +3 k. Then the vector product ( a + b ) ×(( a ×(( a - b ) × b )) × b ) is equal to:

Let $\displaystyle \overrightarrow{\mathrm{a}}=\hat{i}+\hat{j}+2 \hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=-\hat{i}+2 \hat{j}+3 \hat{k}$. Then the vector product $\displaystyle (\vec{a}+\vec{b}) \times((\vec{a} \times((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})$ is equal to: