Math Challenges

Submissions for Problem #35

Compute the dot product of the two given vectors.
What is the angle between them?

\[ \displaylines{\mathbf{a}=<3,1>\\ \mathbf{b}=<1,4>} \]

zapwai

Solution: \( \displaylines{\mathbf{a}\cdot\mathbf{b}=3\cdot1+1\cdot4=7\\ \mathbf{a}\cdot\mathbf{b}=\left|\mathbf{a}\Vert\mathbf{b}\right|\cos\theta\\ \left|\mathbf{a}\right|=\sqrt{10},\left|\mathbf{b}\right|=\sqrt{17}\\ 7=\sqrt{170}\cos\theta\Rightarrow\theta\approx57.53^{\circ}} \)