For three vectors vec u, vec v, vec w which of the following expressi…

We have,

$\vec u.(\vec v×\vec w)=(\vec v×\vec w).\vec u$  [∵ Dot product is commutative]

So, expression in options (1) and (2) are equal.

Since the positions of dot and cross can be interchanged in scalar triple product. Therefore,

$(\vec u×\vec v).\vec w=\vec u.(\vec v×\vec w)$

So, expression in options (1) and (4) are equal.

But, $\vec v.(\vec u×\vec w) = (\vec u×\vec w). \vec v = \vec u. (\vec w×\vec v) = - \vec u. (\vec v×\vec w)$

Hence, expression in (3) is not equal to the remaining three.