This comes from a university pre-session problem list. v and w are vectors.
$|v| = 1$, $|w| = 1$, the angle between $v$ and w is $1.7$ radians. Calculate $|4v + 2w|$.
Using the dot product and breaking brackets, we get the answer $|4v + 2w|=\sqrt{20+16\cos(1.7)}$.
Using the cosine rule, as done here below, $$ \begin{align} a^2 &= b^2 + c^2 - 2bc\cos(A)\\ a^2 &= (4v)^2 + (2w)^2 -2\cdot 2\cdot 4\cos(1.7)\\ a^2 &= 16 + 4 - 16\cos(1.7)\\ &\implies a = \sqrt{20-16\cos(1.7)} \end{align} $$ you get the answer $|4v + 2w|=\sqrt{20-16\cos(1.7)}$, which is incorrect as it should be $+16\cos(1.7)$ inside the square root. This is despite the vectors $v$ and $w$ sharing the same tail ("the angle between $v$ and $w$ is 1.7"), and that only magnitudes are ever used.
What is wrong with the application of the cosine rule here?
Thank you.
Related question, not helpful here: Cosine rule formula proof problem with do product, where does positive sign come from?
