Thank you for reporting, we will resolve it shortly
Q.
Let $\overline{ A }=\hat{ i } A \cos \theta+ \hat {j} A \sin \theta,$ be any vector. Another vector $\overrightarrow{ B }$ which is normal to $\overrightarrow{ A }$ is:
Motion in a Plane
Solution:
For perpendicular condition,
$\overrightarrow{ A } \cdot \overrightarrow{ B }=0$
$\overrightarrow{ A } \cdot \overrightarrow{ B }$
$=(\hat{ i } A \cos \theta+\hat{ j } A \sin \theta)(\hat{ i } B \sin \theta-\hat{ j } B \cos \theta)$
$= A \cos \theta B \sin \theta- A \sin \theta B \cos \theta$
$= AB \sin \theta \cos \theta- AB \sin \theta \cos \theta$
$=0$
$\overrightarrow{ A } \cdot \overrightarrow{ B }=0$ (condition satisfied)