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course Mth 277
7) 9.3.24 Find two distinct unit vectors orthogonal to both v = i + 2j -2k and w = i + j - 2k.The vectors <2,0,1> and <4,0,2> are both orthogonal to both `v and `w, since their dot products result in a value of 0.
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Neither of these is a unit vector.
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To my understanding, the unit vector is equal to the vector divided by the magnitude of the same vector, so:
|<2,0,1>| = sqrt(5) ~= 2.236
|<4,0,2>| = sqrt(18)~= 4.243
<0.89, 0, 0.447> and <0.94, 0, 0.471> are two unit vectors that are orthogonal to both v and w.
If I'm still missing something, please let me know.."
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<2,0,1> is orthogonal to both, so
<2,0,1> / || <2, 0, 1 > || = <2 sqrt(5) / 5, 0, sqrt(5) / 5> is orthogonal to both.
So is
- <2 sqrt(5) / 5, 0, sqrt(5) / 5>
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