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Find u•v where theta is the angle between u and v

Find u•v where theta is the angle between u and v-example-1

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Answer:

88√2 = 124.5 (nearest tenth)

Explanation:


\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}

Given:


  • |u| = 8

  • |v| = 22

  • \theta =(\pi)/(4)

Substitute the given values into the dot product formula:


\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left((\pi)/(4)\right)\\\\&=176 \cdot (√(2))/(2)\right)\\\\&=88√(2)\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}

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