Question

I cannot solve this question no matter how hard I try , I tried many different answers & kept getting 8.04 but it said it was wrong

Answer 1

hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.

`\left < 3(1)/(2)~~,~~4(2)/(3) \right > \hspace{5em}\left < 7(1)/(4)~~,~-8(1)/(2) \right > \\\\[-0.35em] ~\dotfill`

`\stackrel{mixed}{3(1)/(2)}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4(2)/(3)} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7(1)/(4)}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8(1)/(2)} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill`

`\left < 3(1)/(2)~~,~~4(2)/(3) \right > ~~\cdot~~\left < 7(1)/(4)~~,~-8(1)/(2) \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}`