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

Correct answer: B. (1)/(5)( b - 4 a ) Given OP = a and OQ = b . Since OP = 5 OR , we have OR = a 5 . Also, OQ = 5 RM , which gives RM = b 5 . The position vector of M is given by OM = OR + RM = a 5 + b 5 . Now, we need to find PM : PM = OM - OP PM = ( a 5 + b 5 ) - a PM = b - 4 a 5 = (1)/(5)( b - 4 a ) Answer: (1)/(5)( b - 4 a )

JEE Main 20265 AprilEvening Shift

Exam: JEE Main
Year: 2026
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Vector Algebra

JEE Main 2026 · 5 April · Evening Shift · Mathematics · Vector Algebra

Let O be the origin, OP = a and OQ = b . If R is the point on OP...

Let

O

be the origin,

\vec{OP} = \vec{a}

and

\vec{OQ} = \vec{b}

. If

R

is the point on

\vec{OP}

such that

\vec{OP} = 5\vec{OR}

, and

M

is the point such that

\vec{OQ} = 5\vec{RM}

, then

\vec{PM}

is equal to :

Options

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

Correct answer

B. $\dfrac{1}{5}(\vec{b} - 4\vec{a})$

Step-by-step solution

Given

\vec{OP} = \vec{a}

and

\vec{OQ} = \vec{b}

.

Since

\vec{OP} = 5\vec{OR}

, we have

\vec{OR} = \dfrac{\vec{a}}{5}

.

Also,

\vec{OQ} = 5\vec{RM}

, which gives

\vec{RM} = \dfrac{\vec{b}}{5}

.

The position vector of

M

is given by

\vec{OM} = \vec{OR} + \vec{RM} = \dfrac{\vec{a}}{5} + \dfrac{\vec{b}}{5}

.

Now, we need to find

\vec{PM}

\vec{PM} = \vec{OM} - \vec{OP}

\vec{PM} = \left(\dfrac{\vec{a}}{5} + \dfrac{\vec{b}}{5}\right) - \vec{a}

\vec{PM} = \dfrac{\vec{b} - 4\vec{a}}{5} = \dfrac{1}{5}(\vec{b} - 4\vec{a})

Answer:

\dfrac{1}{5}(\vec{b} - 4\vec{a})

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