A) \[b\,\sin \,\theta \,\hat{i}+a\,\cos \,\theta \hat{j}\]
B) \[\frac{1}{a}\,\sin \,\theta \,\hat{i}+\frac{1}{b}\,\cos \,\theta \hat{j}\]
C) \[5\hat{k}\]
D) \[\frac{3\,\hat{i}}{a}+\,\cos \,\theta \hat{j}\]
Correct Answer: A
Solution :
[a] Two vector are said to be perpendicular when their dot product is zero Let \[A\,=a\,\cos \,\theta \,\hat{i}+b\ \sin \,\theta \,\hat{j}\] From options, option [a] gives dot product equal to zero \[\vec{A}\,.\vec{B}=\left( a\,\cos \,\theta \hat{i}+b\,\sin \theta \hat{j} \right).\left( b\,Sin\,\theta \hat{i}-a\,Cos\,\theta \,\hat{j} \right)\] \[\left( {\vec{A}} \right)\] \[\left( {\vec{B}} \right)\,(let)\] \[=ab\text{ }sin\,\theta \text{ }cos\,\theta -ab\text{ }sin\,\theta \text{ }cos\,\theta =0\]
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