Question

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

Answer 1

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}`