Answer
(a) 2 (b) -2 (c) -2 (d) 0
Work Step by Step
(a) Given: $u \cdot (v \times w)=2$
$(u \times v) \cdot w=2$
(b) Given: $u \cdot (v \times w)=2$
$u \cdot (w \times v)=u \cdot -(v \times w)$
$-(u \cdot (v \times w))=-2$
Thus, $u \cdot (w \times v)=-2$
(c) Given: $u \cdot (v \times w)=2$
$v \cdot (u \times w) = v \cdot -( w \times u)$
$=-(v \cdot (w \times u)$
$=-((v \times w) \cdot u)$
$=-u \cdot (v \times w)$
Thus, $v \cdot (u \times w) = -2$
(d) Given: $u \cdot (v \times w)=2$
Since $(u \times v) \perp v$; the dot product of the two vectors is $0$.
Thus, $(u \times v) \cdot v=0$
