Question

Find a unit vector u in the direction of v. Verify that u = 1.v = 3, −4

Answer 1

`\text{unit vector = u= <}(3)/(5),(-4)/(5)>`Step-by-step explanation:

v = <3, -4>

`\begin{gathered} \text{unit vector = u = }\frac{v}\text \\ v\text{ = <3, -4>} \\ \mleft\Vert\text{ v }\mright|\text\sqrt[\text{ }]{(3)^2+(-4)^2\text{ }}\text{ =}\sqrt[]{9+16} \\ \Vert\text{ v }|\text =\sqrt[]{25} \\ \Vert\text{ v }|\text = 5 \end{gathered}`
`\begin{gathered} \text{ u = }\frac{<3,\text{ -4>}}{5} \\ unit\text{ vector = <}(3)/(5),(-4)/(5)> \end{gathered}`

Verifying || u || = 1

`\begin{gathered} \text{unit vector = u= <}(3)/(5),(-4)/(5)> \\ \mleft\Vert\text{ u }\mright|\text= \sqrt[]{((3)/(5))^2+((-4)/(5)})^2 \\ =\text{ }\sqrt[]{(9)/(25)+(16)/(25)}\text{ =}\sqrt[]{(9+16)/(25)} \\ \mleft\Vert u\text{ }\mright|\text\sqrt[]{(25)/(25)} \\ \Vert u\text{ }|\text1 \end{gathered}`