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.

May 21, 2026Mathematics

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May 21, 2026

Answer

\vec{r} - \vec{m} $$

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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 $\vec{MR} = \frac{1}{4}\vec{RN}$ , find an expression for r in terms of m and n.

Step 1: Express the vectors $\vec{MR}$ and $\vec{RN}$ in terms of position vectors. $\vec{MR} = \vec{r} - \vec{m}$ $\vec{RN} = \vec{n} - \vec{r}$

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

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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 MR = (1)/(4)RN, find an expression for r in terms of m and n.

Asked on May 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 21, 2026

Here are the solutions to the problems you've provided: 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 MR = (1)/(4)RN, find an expression for r in terms of m and n. Step 1: Express the vectors MR and RN in terms of position vectors. MR = r - m RN = n - r Step 2: Substitute these expressions into the given equation $MR =