JEE PYQ: Vector Algebra - Question ID 9197312924bd (JEE Main 2021)

ID: 9197312924bdJEE Main 2021Single Correct MCQ

Two vectors

{\overrightarrow P }

and

{\overrightarrow Q }

have equal magnitudes. If the magnitude of

{\overrightarrow P + \overrightarrow Q }

is n times the magnitude of

{\overrightarrow P - \overrightarrow Q }

, then angle between

{\overrightarrow P }

and

{\overrightarrow Q }

is :

\left| {\overrightarrow P } \right| = \left| {\overrightarrow Q } \right| = x

..... (i)

\left| {\overrightarrow P + \overrightarrow Q } \right| = n\left| {\overrightarrow P - \overrightarrow Q } \right|

{P^2} + {Q^2} + 2PQ\cos \theta = {n^2}({P^2} + {Q^2} - 2PQ\cos \theta )

Using (i) in above equation

\cos \theta = {{{n^2} - 1} \over {1 + {n^2}}}

\theta = {\cos ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)

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