The figure shows three vectors p,q,and r,wher | vedclass

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(A) In $	riangle OAB$,$C$ is the midpoint of $AB$. By the triangle law of vector addition:In $	riangle OAC$,$\vec{p} = \vec{r} + \vec{AC} \implies \

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$p+q=2r$

Vedclass · Answer

(A) In $	riangle OAB$,$C$ is the midpoint of $AB$. By the triangle law of vector addition:In $	riangle OAC$,$\vec{p} = \vec{r} + \vec{AC} \implies \vec{AC} = \vec{p} - \vec{r}$.In $	riangle OBC$,$\vec{q} = \vec{r} + \vec{BC} \implies \vec{BC} = \vec{q} - \vec{r}$.Since $C$ is the midpoint of $AB$,the vector $\vec{AC}$ is equal to the vector $\vec{CB}$.Therefore,$\vec{AC} = -\vec{BC}$.Substituting the expressions,we get: $\vec{p} - \vec{r} = -(\vec{q} - \vec{r})$.$\vec{p} - \vec{r} = -\vec{q} + \vec{r}$.$\vec{p} + \vec{q} = 2\vec{r}$.Thus,the correct relation is $p+q=2r$.

The figure shows three vectors $p$,$q$,and $r$,where $C$ is the midpoint of $AB$. Which of the following relations is correct?

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