Question
Let \( \vec{x}=\left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right] \) and \( \vec{y}=\left[\begin{array}{c}-2 \\ 5 \\ 5\end{array}\right] \). Then \( \vec{x} \cdot \vec{y}=\square \)
Ask by Patel Tyler. in the United States
Feb 20,2025
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Answer
The dot product of vectors x and y is 11.
Solution
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Bonus Knowledge
To calculate the dot product \( \vec{x} \cdot \vec{y} \), you multiply corresponding components of the vectors and then sum those products: \[ \vec{x} \cdot \vec{y} = (2)(-2) + (1)(5) + (2)(5) = -4 + 5 + 10 \] Now, simplify it: \[ -4 + 5 + 10 = 11 \] Thus, \( \vec{x} \cdot \vec{y} = 11 \).