JEE PYQ: Vector Algebra - Question ID d2b59d7286f2 (JEE Main 2019)

ID: d2b59d7286f2JEE Main 2019Single Correct MCQ
Two vectors A\overrightarrow A and B\overrightarrow B have equal magnitudes. The magnitude of (A+B)\left( {\overrightarrow A + \overrightarrow B } \right) is 'n' times the magnitude of (AB)\left( {\overrightarrow A - \overrightarrow B } \right) . The angle between A{\overrightarrow A } and B{\overrightarrow B } is -

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Step-by-step Explanation

A+B=2acosθ/2\left| {\overrightarrow A + \overrightarrow B } \right| = 2a\cos \theta /2      . . . (1)

AB=2acos(πθ)2=2asinθ/2\left| {\overrightarrow A - \overrightarrow B } \right| = 2a\cos {{\left( {\pi - \theta } \right)} \over 2} = 2a\sin \theta /2      . . . (2)

n(2acosθ2)=2asinθ2\Rightarrow \,\,\,n\left( {2a\cos {\theta \over 2}} \right) = 2a{{\sin \theta } \over 2}

tanθ2=n\Rightarrow \,\,\,\tan {\theta \over 2} = n