MHB S6.12.3.17 Find the angle between the vectors

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The discussion focuses on finding the angle between two vectors, a and b, using the dot product formula. The calculation involves determining the cosine of the angle θ, resulting in a value of approximately 0.1569. This leads to an angle of about 81 degrees when applying the arccosine function. Participants confirm that the working up to the cosine expression is correct. The main concern raised is regarding the interpretation or application of the dot product in the context of the problem.
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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