Question:medium

In a quadrilateral ABCD, $\angle A = \frac{2\pi}{3}$ and AC is the bisector of angle A. If $15|AC| = 5|AD| = 3|AB|$, then the angle between $\vec{AB}$ and $\vec{BC}$ is

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When finding the angle between vectors representing sides of a triangle, be careful about the direction of vectors. The angle 'at' a vertex, say B, is the angle between $\vec{BA}$ and $\vec{BC}$. The angle between $\vec{AB}$ and $\vec{BC}$ is the exterior angle at B. Exam questions often ask for the interior angle even if vectors point outwards.

Updated On: Mar 30, 2026

$\cos^{-1}(\frac{\sqrt{3}}{\sqrt{7}})$
$\cos^{-1}(\frac{3\sqrt{3}}{2\sqrt{7}})$
$\cos^{-1}(\frac{4\sqrt{3}}{5\sqrt{7}})$
$\cos^{-1}(\frac{3\sqrt{3}}{4\sqrt{7}})$

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The Correct Option is B

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