If the magnitude of the moment about the point $\hat j +\hat k$ of a force $\hat i +α\hat j-\hat k$ acting through the point $\hat i + \hat j$ is $\sqrt{8}$, then the value of $α$, is
Answer & explanation
Correct answer: option 2
Let $\vec M$ be the moment of the force $\vec F = \hat i +α\hat j-\hat k$ acting through the point $A (\hat i +\hat j)$ about the point $O(\hat j +\hat k)$.
Then,
$\vec M=\vec{OA}×\vec F$
$⇒\vec M=(\hat i-\hat k)×(\hat i +α\hat j-\hat k)$
$⇒\vec M=\begin{vmatrix}\hat i&\hat j&\hat k\\1&0&-1\\1&α&-1\end{vmatrix}=α\hat i+α\hat k$
$⇒|\vec M|=\sqrt{α^2+α^2}=\sqrt{2}|α|$
$⇒\sqrt{2}|α|=\sqrt{8}$
$⇒|α|=2⇒α=±2$