Question

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

• A. circle passing through $A,B,C$ and $D$
• B. straight line passing through $C$ and $D$
• C. straight line passing through $A$ and $B$
• D. None of these

Answer 1

Answer: (B)

straight line passing through $C$ and $D$

Resultant of the forces represented by vector PA and vector PB is a vector represented by PA vector + PB vector which is 2 PD vector, where D is the middle point of AB. Since A and B are fixed, therefore D is also a fixed point. But the resultant also passes through C which is another given fixed point. Hence, the locus of point P is the straight line joining through C and D.