## Calculus: Early Transcendentals 8th Edition

(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, $(u \times v) \cdot v=0$