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The vectors
u and
v have the same direction.
a. Find
||u||.
b. Find
||v||.
c. Is
u=v ? Explain.

The vectors $\mathbf{u}$ and $\mathbf{v}$ have the same direction. $\newline$ a. Find $\|\mathbf{u}\|$ . $\newline$ b. Find $\|\mathbf{v}\|$ . $\newline$ c. Is $\mathbf{u}=\mathbf{v}$ ? Explain.

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Absolute values of complex numbers

Full solution

Q. The vectors

\mathbf{u}

and

\mathbf{v}

have the same direction.

\newline

a. Find

\|\mathbf{u}\|

.

\newline

b. Find

\|\mathbf{v}\|

.

\newline

c. Is

\mathbf{u}=\mathbf{v}

? Explain.

Assume Magnitude of u: a. To find $||u||$ , we need the components of $u$ , but since they're not given, let's assume $||u||$ is some positive value $x$ . $\newline$ $||u|| = x$
Magnitude of v: b. Since v has the same direction as u, and assuming they have the same magnitude, $||v||$ is also $x$ . $\newline$ $||v|| = x$
Comparison of $u$ and $v$ : c. To determine if $u = v$ , we need to know both their magnitudes and directions. Since they have the same direction and we assumed the same magnitude, $u = v$ .

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