If $\vec α = 2\hat i+ 3\hat j-\hat k, \vec β=−\hat i+2\hat j−4\hat k, \vec γ =\hat i+\hat j+\hat k$, then $(\vec α × \vec β).(\vec α × \vec γ)$ is equal to
Answer & explanation
Correct answer: option 1
We have,
$(\vec α × \vec β).(\vec α × \vec γ)=(\vec α.\vec α)(\vec β.\vec γ)-(\vec α.\vec γ)(\vec β.\vec α)$
$⇒(\vec α × \vec β).(\vec α × \vec γ)=-3×14-8×4=-42-32=-74$