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If $\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$, then the angle between $\overrightarrow{\mathbf{a}}$ and $\vec{b}$ is
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The correct answer is:
$180^{\circ}$
Given, $\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$
$\Rightarrow \quad|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}| \cos \theta=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$
$\Rightarrow \quad \cos \theta=-1$
$\Rightarrow \quad \theta=180^{\circ}$
$\Rightarrow \quad|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}| \cos \theta=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$
$\Rightarrow \quad \cos \theta=-1$
$\Rightarrow \quad \theta=180^{\circ}$
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