Let O be the origin, overrightarrow OP =overrightarrow a and overrightarrow OQ =overrightarrow b . If R is the point on overrightarrow OP such that overrightarrow OP =5 overrightarrow OR , and M is the point such that overrightarrow OQ =5 overrightarrow RM , then overrightarrow PM is equal to:

Mathematics · Vector Algebra

JEE Main 2026 — 5 April, Evening Shift — Question 40

Let O be the origin, $\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{OQ}}=\overrightarrow{\mathrm{b}}$ . If $R$ is the point on $\overrightarrow{\mathrm{OP}}$ such that $\overrightarrow{\mathrm{OP}}=5 \overrightarrow{\mathrm{OR}}$ , and M is the point such that $\overrightarrow{\mathrm{OQ}}=5 \overrightarrow{\mathrm{RM}}$ , then $\overrightarrow{\mathrm{PM}}$ is equal to:

Option A:
$\frac{1}{5}(\vec{a}-4 \vec{b})$
Option B:
$\frac{1}{5}(\vec{b}-4 \vec{a})$
Correct
Option C:
$\frac{1}{5}(-\vec{a}+4 \vec{b})$
Option D:
$\frac{1}{5}(-\vec{b}+4 \vec{a})$

Answer: B

Step-by-step solution

$\overrightarrow{\mathrm{OR}}=\frac{\overrightarrow{\mathrm{OP}}}{5}=\frac{\overrightarrow{\mathrm{a}}}{5}$ $\overrightarrow{\mathrm{RM}}=\frac{\overrightarrow{\mathrm{OQ}}}{5}=\frac{\overrightarrow{\mathrm{b}}}{5}$ $\overrightarrow{\mathrm{OM}}-\overrightarrow{\mathrm{OR}}=\frac{\overrightarrow{\mathrm{b}}}{5}$ $\overrightarrow{\mathrm{OM}}=\frac{\overline{\mathrm{a}}+\overline{\mathrm{b}}}{5}$ $\overrightarrow{\mathrm{PM}}=\overrightarrow{\mathrm{OM}}-\overrightarrow{\mathrm{OP}}$ $\frac{\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}}{5}-\overrightarrow{\mathrm{a}}$ $=\frac{\overrightarrow{\mathrm{b}}-4 \overrightarrow{\mathrm{a}}}{5}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 5 April, Evening Shift
Subject: Mathematics
Chapter: Vector Algebra
Topic: Algebra of Vectors