JEE Main 2026 Apr 5 Shift 2, Mathematics Q16: Basic Concepts of Vector Algebra

JEE Main2026Apr 5, Shift 2Mathematics

Let $O$ be the origin, $O P = a$ and $O Q = b$ . If $R$ is the point on $O P$ such that $O P = 5 O R$ , and $M$ is the point such that $O Q = 5 R M$ , then $P M$ is equal to:

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

Solution

$O R = \frac{O P}{5} = \frac{a}{5}$ and $R M = \frac{O Q}{5} = \frac{b}{5}$ .

$O M = O R + R M = \frac{a + b}{5}$ .

$P M = O M - O P = \frac{a + b}{5} - a = \frac{b - 4 a}{5}$ .

Concept behind this question

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