Question

Find the angle between the following pair of vectors: Around your answers to nearest tenths.p = < -8 , 1 > r = < -4 , 0 >

Answer 1

`\begin{gathered} \cos \text{ }\phi\text{ = }\frac{u\text{ v}} \\ |u|\text{ = }\sqrt[]{-8^2+1^2\text{ }}=\text{ }\sqrt[]{64\text{ + 1}}\text{ = }\sqrt[]{65} \\ |v|\text{ = }\sqrt[]{-4^2+0^2}\text{ = }\sqrt[]{16\text{ }}\text{ = }\sqrt[]{16} \\ \cos \text{ }\phi\text{ = }\frac{(-8\cdot-4)\text{ + (1}\cdot0)}{\sqrt[]{65\text{ }}\cdot\sqrt[]{16}} \\ \cos \text{ }\emptyset\text{ = }\frac{32\text{ 1}}{4\sqrt[]{65}} \\ \cos \text{ }\emptyset\text{ = }\frac{32}{4\sqrt[]{65}} \\ \cos \text{ }\emptyset\text{ = }0.99 \\ \emptyset\text{ = 7.1} \end{gathered}`

Angle = 7.1°