Suppose that u,vu,v and w are vectors such that ⟨u,v⟩=6, ⟨v,w⟩=−7, ⟨u,w⟩=13⟨ ∣∣u∣∣=1,∣∣v∣∣=6,∣∣w∣∣=19∣∣u∣∣=1, given expression ⟨u+v,u+w⟩.

postillan4 2021-02-05 Answered

Suppose that u,vu,v and w are vectors such that \(⟨u,v⟩=6, ⟨v,w⟩=−7, ⟨u,w⟩=13∣∣u∣∣=1,∣∣v∣∣=6,∣∣w∣∣=19∣∣u∣∣=1\), given expression ⟨u+v,u+w⟩.

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Expert Answer

Velsenw
Answered 2021-02-06 Author has 21625 answers

Given that u,v and w are vectors such that \(\displaystyle{\left({u},{v}\right)}={6},{\left({v},{w}\right)}=-{7},{\left({u},{w}\right)}={13},{\left|{\left|{u}\right|}\right|}={1},{\left|{\left|{v}\right|}\right|}={6},{\left|{\left|{w}\right|}\right|}={19}\)
\((u+v,v+w)=(u,v)+(u,w)+(v,v)+(v,w) =6+13+(6^2)-7\)

\(=12+36 =48.\)
Again \(\displaystyle{\left({u}+{v},{u}+{w}\right)}={\left({u},{u}\right)}+{\left({u},{w}\right)}+{\left({v},{u}\right)}+{\left({v},{w}\right)}\) =1+13+6-7 =13.

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