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Question

A,B,C are fixed points and P is a variable point such that the resultant of forces at P represented by PA and PB always passes through C and D is the mid-point of AB, then locus of P is

A
circle passing through A,B,C and D
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B
straight line passing through C and D
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C
straight line passing through A and B
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D
none of these
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Solution

The correct option is C straight line passing through C and D
Resultant of forces represented by ¯PA and ¯PB i.e. by 2¯PD where D is the middle point of AB. Since A and B are fixed. Thus D is also fixed point. But the resultant also passed through C, another fixed point. Hence the locus of P is a straight line joining C and D
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