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QuestionMathematics

What is the dot product of 2i+ 4j+ 5k and 3i+ 2j+k?
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Answer

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Step 1:
: Recall the definition of the dot product.

\vec{a} \cdot \vec{b} = a\_1b\_1 + a\_2b\_2 + a\_3b\_3

Step 2:
: Identify the components of the vectors given in the problem.

\vec{b} = 3\vec{i} + 2\vec{j} + \vec{k}
We have: and

Step 3:
: Apply the formula for the dot product using the components of the vectors.

\vec{a} \cdot \vec{b} = (2)(3) + (4)(2) + (5)(1)

Step 4:
: Calculate the result.

\vec{a} \cdot \vec{b} = 6 + 8 + 5 = 19

Final Answer

\boxed{\vec{a} \cdot \vec{b} = 19}.