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

rocedwrp 2021-01-15 Answered

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

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## Expert Answer

Yusuf Keller
Answered 2021-01-16 Author has 90 answers
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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