A) 1
B) 2
C) \[\frac{1}{2}\]
D) \[\frac{3}{2}\]
Correct Answer: C
Solution :
Given\[|P+Q|=\sqrt{3}\] \[\Rightarrow \] \[{{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta =3\] \[\Rightarrow \] \[{{1}^{2}}+{{1}^{2}}+2\times 1\times 1\cos \theta =3\] \[\therefore \] \[\cos \theta =\frac{1}{2}\] Now\[(P-Q)(2P+Q)=2P.P+P.Q-2Q.P-Q.Q\] \[=2{{(1)}^{2}}-1\times 1\cos \theta -{{1}^{2}}\] \[=2-\frac{1}{2}-1=\frac{1}{2}\]
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