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Find the length and direction (when defined) of \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u}\). \(\mathbf{u} = -6\mathbf{i}\), \(\mathbf{v} = 8\mathbf{j}\)

          Find the length and direction (when defined) of \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u}\).
\(\mathbf{u} = -6\mathbf{i}\), \(\mathbf{v} = 8\mathbf{j}\)
        
Find the length and direction (when defined) of ๐ฎร—๐ฏ and ๐ฏร—๐ฎ.
๐ฎ = -6๐ข, ๐ฏ = 8๐ฃ

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the length and direction (when defined) of u imes v and v imes u. u=-6i,v=8j Find the length and direction(when defined of u xv and vx u K u=-6iv=8j
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Transcript

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00:01 Hello, we have u is equal to this vector, v equal to this vector and u cross v is equal to the cross product of u and v is equal to i j k times i j k minus 2 minus 2 minus 3 5 5.
00:30 So, to find the cross product of these two vectors, we take the determinant of this matrix, which is equal to i times minus 2 times 3 is minus 6 minus minus 3 times 5 is minus 15.
00:47 So, minus 6 minus minus 15 is minus 6 plus 15, which is minus 6, which is equal to 9 minus 6 plus 15, which is equal to 9.
01:01 So, we have 9 i plus j times minus 3 5 is minus 15 minus minus 2 3, which is minus minus 6.
01:13 So, minus 15 plus 6, which is minus 9 plus k times minus 2 5, which is minus 10 minus minus 2 5, which is minus 10.
01:28 So, minus 10 minus minus 10, which is minus 10 plus 10.
01:33 So, minus 10 plus 10 is 0.
01:36 So, this vector is 9 i minus 9 j.
01:51 Okay, so we find u cross v is the vector 9 i minus 9 j...
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