A) \[b\sin \theta \hat{i}-a\cos \theta \hat{j}\]
B) \[\frac{1}{2}\sin \theta \hat{i}-\frac{1}{b}\cos \theta \hat{j}\]
C) \[5k\]
D) all of the above
Correct Answer: D
Solution :
From definition of dot product of vectors, we have \[x.y=xy\cos \theta \] When \[\theta ={{90}^{o}},\cos {{90}^{o}}=0\] \[\therefore \] \[x.y=0\] Given, \[x=a\cos \theta \hat{i}+b\sin \theta \hat{j}\] \[y=b\sin \theta \hat{i}-a\cos \theta \hat{j}\] \[x.y=(a\cos \theta \hat{i}-b\sin \theta \hat{j})\] \[(b\sin \theta \hat{i}.a\cos \theta \hat{j})\] \[x.y=ab\sin \theta \cos \theta -ab\sin \theta \cos \theta =0\] Hence, vacuous are perpendicular. Similarly for option and also\[x.y=0\]
You need to login to perform this action.
You will be redirected in
3 sec
