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If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three non-collinear points and $k \mathbf{a}+2 \mathbf{b}+3 \mathbf{c}$ is a point in the plane of $\mathbf{a}, \mathbf{b}, \mathbf{c}$, then $k=$
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The correct answer is:
-5
$\mathbf{a}, \mathrm{b}$ and $\mathrm{c}$ are three non-colline ar point and $k \mathbf{a}+2 \mathbf{b}+3 \mathbf{c}$ is a point in the plane $\mathbf{a}, \mathbf{b}, \mathbf{c}$
$$
\begin{aligned}
& \therefore k \mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0 \\
& \Rightarrow \quad k+2+3=0 \Rightarrow k=-5
\end{aligned}
$$
$$
\begin{aligned}
& \therefore k \mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0 \\
& \Rightarrow \quad k+2+3=0 \Rightarrow k=-5
\end{aligned}
$$
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