Study guide and
2 practice problems
on:
Component view of vector-scalar multiplication
$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
In terms of components, $c \langle x_1, x_2, x_3 \rangle = \langle c x_1, c x_2, c x_3 \rangle.$
Related topics
Vector scalar multiplication
(13 problems)
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Practice problems
For a scalar $c$ and a vector $\bfx$, show that $\left |c\bfx \right| = \left |c\right | \ \left |\bfx \right|.$
Solution
Find a unit vector in the direction of $\langle 1, 1 \rangle$.
Solution