S6.12.3.17 Find the angle between the vectors

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SUMMARY

The discussion focuses on calculating the angle between two vectors, \( a = \langle 3, -1, 5 \rangle \) and \( b = \langle -2, 4, 3 \rangle \), using the cosine formula derived from the dot product. The calculation shows that \( \cos(\theta) \approx 0.1569 \), leading to an angle of approximately \( 81^\circ \) after applying the arccosine function. The participants confirm that the working up to the cosine expression is accurate, addressing concerns about the dot product's application in this context.

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karush
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$\tiny{s6.12.3.17}\\$
$\textsf{ Find the angle between the vectors $a$ and $b$}\\$
\begin{align}
\displaystyle
a&=\langle 3,-1,5\rangle &b&=\langle -2,4,3\rangle\\
\\
\cos\left({\theta}\right)&=\frac{(3\cdot -2)+(-1\cdot4)+(5\cdot3)}
{|\sqrt{35}|\cdot|\sqrt{29}|}\\
&\approx 0.1569 \\
\arccos(0.1569)&\approx80.97^o\approx81^o
\end{align}
tried W|A but dot product ?
 
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This looks correct. What's the problem exactly?
 
What about the dot product are you referring to?

The working, at least up to the expression for cosine of theta, is correct.
 

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