## niyaz 8 months ago In the session 10 problems, 1b, we use the dot product to get the angle between Av and v. In the solutions, I don't understand how they get that (Av dot v) / |Av||v| =1/sqrt(2). I understand that the length is sqrt(x^2+y^2) and the dot product is (x^2+y^2)/sqrt(2).

1. hanson.char

\begin{aligned} Av\cdot v &= |Av||v|\cos\theta \\ \therefore \cos\theta &= \frac{\color{blue}{Av\cdot v}}{\color{red}{|Av|}\color{teal}{|v|}} \\ &= \color{blue}{\frac{x^2+y^2}{\sqrt{2}}} \cdot \frac{1} {\color{red}{\sqrt{x^2+y^2}}\color{teal}{\sqrt{x^2+y^2}}} \\ &= \frac{x^2+y^2}{\sqrt{2}} \cdot \frac{1} {x^2+y^2} \\ &= {1 \over \sqrt{2}} \end{aligned}

2. niyaz

Oh! thanks. |dw:1403418695064:dw|