Coordinates of the foot of the perpendicular drawn from (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are [IIT 1982]

\[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\]

\[\left( \frac{a}{2},\frac{b}{2} \right)\]

\[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\]

Coordinates of the foot of the perpendicular drawn from (0,0

1.	Coordinates of the foot of the perpendicular drawn from (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are [IIT 1982]
A.	\[\left( \frac{a}{2},\frac{b}{2} \right)\]
B.	\[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\]
C.	\[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\]
D.	None of these
Answer» C. \[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\]

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Coordinates of the foot of the perpendicular drawn from (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are [IIT 1982]

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