If vector(a) = αi + βj + 3k, vector(b) = -βi - αj - k and vector(c) = i - 2j - k

Question

If \(\vec{a} = \alpha \hat{i}+\beta \hat{j}+3\hat{k},\)

\(\vec{b} = -\beta \hat{i}-\alpha \hat{j}-\hat{k}\) and

\(\vec{c} = \hat{i}-2\hat{j}-\hat{k}\)

such that \(\vec{a}.\vec{b}=1\) and \(\vec{b}.\vec{c}=-3,\) then \(\frac{1}{3}\big((\vec{a}\times \vec{b}\big).\vec{c}\big)\) is equal to _______.

Answer 1

Answer is (2)