Study guide and
3 practice problems
on:
Component view of vector subtraction
$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
In terms of components components, $\langle y_1, y_2\rangle - \langle x_1, x_2\rangle = \langle y_1-x_1, y_2-x_2\rangle$.
Related topics
Vector subtraction
(20 problems)
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Practice problems
A river flows with speed $10$ m/s in the northeast direction. A particular boat can propel itself at speed $20$ m/s relative to the water. In which direction should the boat point in order to travel due west.?
Solution
Find the area of the triangle in 3-space between $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$.
Solution
Write down the vector field $\mathbf{F}(x,y)$ whose value at $(x,y)$ is of unit length and points toward $(1,0)$.
Solution