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# Need some help

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Let u, v and w be vectors satisfying

u*v=3, u*w=4, v*w=5.

Then what are

(u+2v)*w, (w-u)*v, (3v-2w)*u

equal to? Enter the list in the order above

Jul 6, 2019

#1
+25528
+2

Let u, v and w be vectors satisfying

$$u*v=3, u*w=4, v*w=5$$.

Then what are

$$(u+2v)*w, (w-u)*v, (3v-2w)*u$$

equal to?

$$\begin{array}{|rcll|} \hline && \mathbf{ (u+2v)*w} \\ &=& u*w+2v*w \\ &=& 4+ 2*5 \\ &=& \mathbf{14} \\ \hline && \mathbf{(w-u)*v} \\ &=& w*v-u*v \\ &=& 5 -3 \\ &=& \mathbf{2} \\ \hline && \mathbf{(3v-2w)*u} \\ &=& 3v*u-2w*u \\ &=& 3*3-2*4 \\ &=& \mathbf{1} \\ \hline \end{array}$$

Jul 6, 2019

#1
+25528
+2

Let u, v and w be vectors satisfying

$$u*v=3, u*w=4, v*w=5$$.

Then what are

$$(u+2v)*w, (w-u)*v, (3v-2w)*u$$

equal to?

$$\begin{array}{|rcll|} \hline && \mathbf{ (u+2v)*w} \\ &=& u*w+2v*w \\ &=& 4+ 2*5 \\ &=& \mathbf{14} \\ \hline && \mathbf{(w-u)*v} \\ &=& w*v-u*v \\ &=& 5 -3 \\ &=& \mathbf{2} \\ \hline && \mathbf{(3v-2w)*u} \\ &=& 3v*u-2w*u \\ &=& 3*3-2*4 \\ &=& \mathbf{1} \\ \hline \end{array}$$

heureka Jul 6, 2019