Vectors 2

Components and Column Vectors:

The Unit Vector:

• has magnitude of: 1
• any direction
• For every Vector $\underline{a}$, There is a Unit Vector in the same direction, $\underline{\hat{a}}$
• $\underline{\hat{a}}=\frac{\underline{a}}{|\underline{a}|}$

Component form:

• $\underline{i}$ = unit vector in +x direction

• $\underline{j}$ = unit vector in +y direction

• Vectors can be represented by their sum(s) of $\underline{i}$ and $\underline{j}$

  • e.g.:

Column Vector notation:

• $\underline{a}=x\underline{i}+y\underline{j}$ (component form)
  • $\underline{a}=\overrightarrow{[x,y]}$ (wonky latex solution idk)