I'm trying to find the angle between these two vectors. I know how to find the angle of using the dot product over magnitude of both vectors. However, these two vectors are opposite to each other, creating an angle of 180 degrees and a dot product of -29. Is there a difference between column vectors and row vectors when using this formula?
v = <-5,2> w = <5,-2> (in column form)
What is going on?
Best Answer
\begin{align} u&=(-5,2)^T\\v&=(5,-2)^T\\ \cos(\theta)&=\dfrac{u^Tv}{||u||\times ||v||}\\ &=\dfrac{-29}{\sqrt{29}\times \sqrt{29}}\\ &=-1\\ \implies \theta&=180 \end{align}