\overrightarrow A and \overrightarrow B are two vectors and \theta is the angle between them, if | \overrightarrow A \times \overrightarrow B | = \sqrt 3 ( \overrightarrow A .\overrightarrow B ), the value of \theta is

Motion in A Plane question

2007 · Q132

Motion in A Plane question

2007 · Q132

View written solutionFree

Correct answer: D

$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \left( {\overrightarrow A .\overrightarrow B } \right)$

$\therefore$ $AB\sin \theta = \sqrt 3 AB\cos \theta$

or $\tan \theta = \sqrt 3$ or $\theta = {\tan ^{ - 1}}\sqrt 3 = 60^\circ$ ;

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Motion in A Plane question

2007 · Q132

Motion in A Plane question

2007 · Q132

View written solutionFree

Correct answer: D

$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \left( {\overrightarrow A .\overrightarrow B } \right)$

$\therefore$ $AB\sin \theta = \sqrt 3 AB\cos \theta$

or $\tan \theta = \sqrt 3$ or $\theta = {\tan ^{ - 1}}\sqrt 3 = 60^\circ$ ;