Question

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]

Answer 1

@Mehek14
@pooja195
@SithsAndGiggles
@Agl202

Answer 2

here are the vector \(A \times B\) and the length of vector \(A\) and the length of the vector \(B\):
\[ \begin{gathered}
A \times B = \left| {\begin{array}{*{20}{c}}
{{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\
{ - 4}&7&{ - 3} \\
8&{ - 11}&8
\end{array}} \right| = {\mathbf{\hat x}}\left( {56 + 33} \right) - {\mathbf{\hat y}}\left( { - 32 + 24} \right) + {\mathbf{\hat z}}\left( {44 - 56} \right) \hfill \\
\hfill \\
\left| A \right| = \sqrt {16 + 49 + 9} ,\quad B = \sqrt {64 + 121 + 64} \hfill \\
\end{gathered} \]

Answer 3

oops.. here is*...

Answer 4

next, you have to compute the length of the vector \(A \times B\)

Answer 5

oops.. I have made a typo, here is the right formula:
\[A \times B = \left| {\begin{array}{*{20}{c}}
{{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\
{ - 4}&7&{ - 3} \\
8&{ - 11}&8
\end{array}} \right| = {\mathbf{\hat x}}\left( {56 - 33} \right) - {\mathbf{\hat y}}\left( { - 32 + 24} \right) + {\mathbf{\hat z}}\left( {44 - 56} \right)\]

Answer 6

namely it is \((56-33)\) the x-component of \(A \times B\)

Answer 7

I keep getting the same wrong answer for some reason

Answer 8

i fixed it. I got theta = 11.53

Answer 9

yes it was correct :). Thanks !

Answer 10

I got the subsequent results:
\[\begin{gathered}
\left| A \right| = \sqrt {16 + 49 + 9} = \sqrt {74} ,\quad B = \sqrt {64 + 121 + 64} = \sqrt {249} \hfill \\
\hfill \\
A \times B = \left( {23,8, - 12} \right),\quad \left| {A \times B} \right| = \sqrt {737} \hfill \\
\hfill \\
\arcsin \left( {\frac{{\sqrt {737} }}{{\sqrt {74} \cdot \sqrt {249} }}} \right) \approx 11.54^\circ \hfill \\
\end{gathered} \]