Question

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

Vectors and spaces
ANSWERED
asked 2021-01-15

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

Answers (1)

2021-01-16
Now
\(\displaystyle∥{m}+{3}{n}∥^{{{2}}}=⟨{m}+{3}{n},{m}+{3}{n}⟩=⟨{m},{m}⟩+⟨{m},{3}{n}⟩+⟨{3}{n},{m}⟩+⟨{3}{n},{3}{n}⟩=∥{m}∥^{{{2}}}+{6}⟨{m},{n}⟩+{9}∥{n}∥^{{{2}}}={16}+{6}×{135}+{18}={16}+{6}×{135}+{18}={844}\)
Therefore
\(\displaystyle∥{m}+{3}{n}∥=\sqrt{{{844}}}\)
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