What is || <1, 6, -3 > - < 4, -2, -9 >||||<1,6,−3>−<4,−2,−9>||?

1 Answer
Steve M
Apr 13, 2017

||<<1, 6, -3>> - <<4, -2, -9>>|| = sqrt( 109 )||⟨1,6,−3⟩−⟨4,−2,−9⟩||=√109

Explanation:

Let:

vec u = <<1, 6, -3>> - <<4, -2, -9>>→u=⟨1,6,−3⟩−⟨4,−2,−9⟩

First we will simplify the vector:

vec u = <<(1)-(4), (6)-(-2), (-3)-(-9)>> →u=⟨(1)−(4),(6)−(−2),(−3)−(−9)⟩
" " = <<-3, 8, 6>> =⟨−3,8,6⟩

Then we compute the norm:

||vec u|| = sqrt( (-3)^2+(8)^2+(6)^2) ∣∣∣∣→u∣∣∣∣=√(−3)2+(8)2+(6)2
" " = sqrt( 9+64+36 ) =√9+64+36
" " = sqrt( 109 ) =√109

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