Question

Let $\vec{a}=6\hat{i} +9\hat{j}+12\hat{k}, \vec{b} = a\hat{i} +11\hat{j}-2\hat{k}$ and $\vec{c}$ be vectors such that $\vec{a}\times\vec{c}=\vec{a}\times\vec{b}$.
If $\vec{a}.\vec{c}=12,\vec{c}.(\hat{i}-2\hat{j}+\hat{k})=5,$, then $\vec{c}.(\hat{i}+\hat{j}+\hat{k})$ is equal to__________.

Answer 1

The answer is:11