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For the following three vectors, calculate \(3 \cdot (C \cdot (2 \times (A \times B)))\):

\[ A = 4.00 \hat{i} + 3.00 \hat{j} - 3.00 \hat{k} \]

\[ B = -3.00 \hat{i} + 2.00 \hat{j} + 4.00 \hat{k} \]

\[ C = 8.00 \hat{i} - 9.00 \hat{j} \]

Provide your answer with the appropriate number of units.

Answer :

So the value of the vector product 3C . (2A × B) = 1242.

Given that the vectors are,

A = 4 i + 3 j - 3 k

B = - 3 i + 2 j + 4 k

C = 8 i - 9 j

So, now calculating the required we get,

2A = 2 (4 i + 3 j - 3 k) = 8 i + 6 j - 6 k

3C = 3 (8 i - 9 j) = 24 i - 27 j

So, cross product is given by,

2A × B

= [tex]\left[\begin{array}{ccc}i&j&k\\8&6&-6\\-3&2&4\end{array}\right][/tex]

= [(6) (4) - (2) (- 6)] i - [(8) (4) - (- 3) (- 6)] j + [(8) (2) - (- 3) (6)] k

= [24 + 12] i - [32 - 18] j + [16 + 18] k

= 36 i - 14 j + 34 k

So the dot product is given by

3C . (2A × B) = (24 i - 27 j) . (36 i - 14 j + 34 k ) = 24 * 36 + (- 27) * (- 14) = 1242

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The question is not clear. The clear question will be -

"For the following three vectors, what is 3⋅C⋅(2A × B)?

A=4.00i+3.00j−3.00k; B=−3.00i+2.00j+4.00k; C=8.00i−9.00 j"

Thanks for taking the time to read For the following three vectors calculate 3 cdot C cdot 2 times A times B A 4 00 hat i 3 00 hat j 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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