Q.6 Which of the following vectors is perpendicular to vector \( (\hat{\imath} Q \sin \theta-\hat{\jmath} \operatorname{Pcos} \theta) \) (a) \( \hat{\imath} P \cos \theta+\hat{\jmath} Q \sin \theta \) 4b) \( \hat{\imath} \operatorname{Qcos} \theta-\hat{\jmath} P \sin \theta \) (c) \( \hat{\imath} P \sin \theta+\hat{\jmath} Q \cos \theta \) (d) \( \hat{\imath} Q \sin \theta-\hat{\jmath} P \cos \theta \)
Q.6 Which of the following vectors is perpendicular to vector \( (\hat{\imath} Q \sin \theta-\hat{\jmath} \operatorname{Pcos} \theta) \) (a) \( \hat{\imath} P \cos \theta+\hat{\jmath} Q \sin \theta \) 4b) \( \hat{\imath} \operatorname{Qcos} \theta-\hat{\jmath} P \sin \theta \) (c) \( \hat{\imath} P \sin \theta+\hat{\jmath} Q \cos \theta \) (d) \( \hat{\imath} Q \sin \theta-\hat{\jmath} P \cos \theta \)
1 Answers
Given vector \(\vec A\) = (\(\hat i\) θ sin θ - \(\hat j\) P cos θ)
option (a) (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)
Let \(\vec B\) = (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)
Perpendicular condition
\(\vec A.\vec B=0\)
= (\(\hat i\) θ sin θ - \(\hat j\) P cos θ) . (\(\hat i\) P cos θ + \(\hat j\) θ sin θ)
= P θ sin θ cos θ - P θ sin θ cos θ
\(\vec A.\vec B=0\)
option (a) is correct.