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## Homework Statement

>There are three vector $$ \vec a ,\vec b, \vec c$$ in three-dimensional real vector space, and the inner product between them $$\vec a . \vec a=\vec b.\vec b=\vec a.\vec c=1, \vec a.\vec b=0, \vec c.\vec c=4 $$ When setting $$x = \vec b.\vec c$$ ,

(dot here means dot product)

answer the following question: when $$ \vec a ,\vec b, \vec c$$ are linearly dependent, find all possible values of $$ x$$

## Homework Equations

3. The Attempt at a Solution

3. The Attempt at a Solution

For dependent condition

$$\begin{align}

(a×b)·c &= 0\\

a·(b×c) &= 0\\

a(bc \sin θ)&=0

\end{align}$$

So ## \theta= 0## and ##\pi##

Then

$$\begin{align}

x&=|b||c| \cos \theta \\

x&=2 \cos \theta \\

\implies x &= 2 \cos 0, x = 2 \cos \pi \\

x &= \mp 2

\end{align}$$

Am I right?

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