*(Vector algebra, not differential equations --- included as extracted.)*
Let a=i^−αj^+βk^, b=3i^+βj^−αk^, c=−αi^−2j^+k^, α,β∈Z. If a⋅b=−1 and b⋅c=10, then (a×b)⋅c is \_\_\_\_\_\_.
Answer: 9
Solutions · 1
Official solution
Solving 3−2αβ=−1⇒αβ=2, and −3α−2β−α=10⇒2α+β=−5: gives α=−2,β=−1.
\[(\vec a\times\vec b)\cdot\vec c = \begin{vmatrix}1&2&-1\\3&-1&2\\-2&-2&1\end{vmatrix} = 9.\]