blackstreet23
  • blackstreet23
Two vectors are given by vector A = -4i + 7j - 3k and vector B = 8i - 11j + 8k. Evaluate the following quantities. sin-1[|vector A cross product vector B|/ AB]
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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blackstreet23
  • blackstreet23
blackstreet23
  • blackstreet23
@Mehek14 @pooja195 @SithsAndGiggles @Agl202
Michele_Laino
  • Michele_Laino
here are the vector \(A \times B\) and the length of vector \(A\) and the length of the vector \(B\): \[ \begin{gathered} A \times B = \left| {\begin{array}{*{20}{c}} {{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\ { - 4}&7&{ - 3} \\ 8&{ - 11}&8 \end{array}} \right| = {\mathbf{\hat x}}\left( {56 + 33} \right) - {\mathbf{\hat y}}\left( { - 32 + 24} \right) + {\mathbf{\hat z}}\left( {44 - 56} \right) \hfill \\ \hfill \\ \left| A \right| = \sqrt {16 + 49 + 9} ,\quad B = \sqrt {64 + 121 + 64} \hfill \\ \end{gathered} \]

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Michele_Laino
  • Michele_Laino
oops.. here is*...
Michele_Laino
  • Michele_Laino
next, you have to compute the length of the vector \(A \times B\)
Michele_Laino
  • Michele_Laino
oops.. I have made a typo, here is the right formula: \[A \times B = \left| {\begin{array}{*{20}{c}} {{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\ { - 4}&7&{ - 3} \\ 8&{ - 11}&8 \end{array}} \right| = {\mathbf{\hat x}}\left( {56 - 33} \right) - {\mathbf{\hat y}}\left( { - 32 + 24} \right) + {\mathbf{\hat z}}\left( {44 - 56} \right)\]
Michele_Laino
  • Michele_Laino
namely it is \((56-33)\) the x-component of \(A \times B\)
blackstreet23
  • blackstreet23
blackstreet23
  • blackstreet23
I keep getting the same wrong answer for some reason
blackstreet23
  • blackstreet23
i fixed it. I got theta = 11.53
blackstreet23
  • blackstreet23
yes it was correct :). Thanks !
Michele_Laino
  • Michele_Laino
I got the subsequent results: \[\begin{gathered} \left| A \right| = \sqrt {16 + 49 + 9} = \sqrt {74} ,\quad B = \sqrt {64 + 121 + 64} = \sqrt {249} \hfill \\ \hfill \\ A \times B = \left( {23,8, - 12} \right),\quad \left| {A \times B} \right| = \sqrt {737} \hfill \\ \hfill \\ \arcsin \left( {\frac{{\sqrt {737} }}{{\sqrt {74} \cdot \sqrt {249} }}} \right) \approx 11.54^\circ \hfill \\ \end{gathered} \]

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