IIT JEE , AIEEE Forum - Mathematics , Vectors - Radon challenger series Part-5

Radon222

$\vec{BA}=\vec{BC}-\vec{AC} \\ \\ =\left( \frac{\vec{e}}{|\vec{e}|}-\frac{\vec{f}}{|\vec{f}|}\right)-\left(\frac{2\vec{e}}{|\vec{e}|}\right)\\ \\ -\left( \frac{\vec{e}}{|\vec{e}|}+\frac{\vec{f}}{|\vec{f}|}\right)\\ \\ Now.\vec{BA}.\vec{BC}=-\left( \frac{\vec{e}}{|\vec{e}|}+\frac{\vec{f}}{|\vec{f}|}\right)\left( \frac{\vec{e}}{|\vec{e}|}-\frac{\vec{f}}{|\vec{f}|}\right) \\ \\ =-\left(\frac{e^2}{e^2}-\frac{f^2}{f^2}\right)=-(1-1)=0 \\ \\ \rightarrow \angle B =90 \\ \\ \rightarrow cos2A+cos2C=2cos(A+C)cos(A-C)=0\\ \\ \rightarrow cos2A+cos2C+cos2B=-1 \\ \\ \text{This condition also holds true when angle C=90}\\$

Thus both assertion and reason are correct but the reason is not correct explanation of assertion.Therefore the answer is B

Ask & Discuss Questions with Community & Experts