rocedwrp

2021-01-15

It is given: $\parallel m\parallel =4,\parallel n\parallel =\sqrt{2},⟨m,n⟩=135$ find the norm of the vector $m+3n$.

Yusuf Keller

Now
$\parallel m+3n{\parallel }^{2}=⟨m+3n,m+3n⟩=⟨m,m⟩+⟨m,3n⟩+⟨3n,m⟩+⟨3n,3n⟩=\parallel m{\parallel }^{2}+6⟨m,n⟩+9\parallel n{\parallel }^{2}=16+6×135+18=16+6×135+18=844$
Therefore
$\parallel m+3n\parallel =\sqrt{844}$

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