The position vectors of the points A and B ar | vedclass

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(A) Given the position vector of point $C$ is $\vec{OC} = \frac{1}{2}\vec{a} + \frac{1}{3}\vec{b}$.Let $D$ be a point on $OA$ such that $\vec{OD} = \f

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$C$ lies inside $	riangle OAB$

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(A) Given the position vector of point $C$ is $\vec{OC} = \frac{1}{2}\vec{a} + \frac{1}{3}\vec{b}$.Let $D$ be a point on $OA$ such that $\vec{OD} = \frac{1}{2}\vec{a}$. Since $0 Let $E$ be a point on $OB$ such that $\vec{OE} = \frac{1}{3}\vec{b}$. Since $0 By the parallelogram law of vector addition, $\vec{OC} = \vec{OD} + \vec{OE}$ represents the diagonal of the parallelogram $ODCE$.Since $D$ lies on $OA$ and $E$ lies on $OB$, the entire parallelogram $ODCE$ lies within the triangle $OAB$.Therefore, the point $C$ lies inside $	riangle OAB$.

The position vectors of the points $A$ and $B$ are $\vec{a}$ and $\vec{b}$ respectively. If the position vector of the point $C$ is $\frac{\vec{a}}{2} + \frac{\vec{b}}{3}$, then:

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