If C is the mid-point of line segment AB and | vedclass

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(C) Since $C$ is the mid-point of the line segment $AB$,the position vector of $C$ is given by $\vec{c} = \frac{\vec{a} + \vec{b}}{2}$.In terms of vec

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$PA - PC = PC - PB$

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(C) Since $C$ is the mid-point of the line segment $AB$,the position vector of $C$ is given by $\vec{c} = \frac{\vec{a} + \vec{b}}{2}$.In terms of vectors from point $P$,we have $\vec{PC} = \frac{\vec{PA} + \vec{PB}}{2}$.Multiplying by $2$,we get $2\vec{PC} = \vec{PA} + \vec{PB}$.Rearranging the terms,we can write $\vec{PA} - \vec{PC} = \vec{PC} - \vec{PB}$.Thus,the correct relation is $\vec{PA} - \vec{PC} = \vec{PC} - \vec{PB}$.

If $C$ is the mid-point of line segment $AB$ and $P$ is any point not on the line $AB$,then

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