Q104 / 180 · KCET 2009 · Mathematics

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

  • A
    $45^{\circ}$
  • Correct answer
    B
    $180^{\circ}$
  • C
    $90^{\circ}$
  • D
    $60^{\circ}$

Solution

Given, $\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$ $\Rightarrow \quad|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}| \cos \theta=-|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|$ $\Rightarrow \quad \cos \theta=-1$ $\Rightarrow \quad \theta=180^{\circ}$

Hence, the correct answer is option: 'B'.

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