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The position vector M, N and R from the origin are m, n and r respectively. If OMN is a triangle and R is a point on MN such that MR = (1)/(4)RN, find an expression for r in terms of m and n.

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Q1) The position vector M, N and R from the origin are m, n and r respectively. If OMN is a triangle and R is a point on MN such that MR⃗=14RN⃗\vec{MR} = \frac{1}{4}\vec{RN}, find an expression for r in terms of m and n.

  1. Express the vectors MR⃗\vec{MR} and RN⃗\vec{RN} in terms of position vectors.

    MR⃗=r⃗−m⃗\vec{MR} = \vec{r} - \vec{m} RN⃗=n⃗−r⃗\vec{RN} = \vec{n} - \vec{r}

  2. Substitute these expressions into the given equation $\vec{MR} =

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