JEE Main 2026 · 5 Apr · Shift 2 · Mathematics Q16

← JEE Main 2026 · 5 Apr · Shift 2

MathematicsSingle correct+4 / -1Question 16 of 75

Let O be the origin, $\overrightarrow{OP}=\vec a$ and $\overrightarrow{OQ}=\vec b$ . 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 :

\dfrac15\left(\vec a-4\vec b\right)

\dfrac15\left(\vec b-4\vec a\right)

\dfrac15\left(-\vec a+4\vec b\right)

\dfrac15\left(-\vec b+4\vec a\right)

Answer and worked solution

Official answer: B

Points.

$\overrightarrow{OR}=\tfrac15\vec a$ .
$\overrightarrow{RM}=\tfrac15\vec b$ , so $\overrightarrow{OM}=\tfrac15(\vec a+\vec b)$ .

So
$\overrightarrow{PM}=\tfrac15(\vec a+\vec b)-\vec a=\tfrac15\left(\vec b-4\vec a\right).$

(B)

Topics:Vector operations

← Previous question Next question →

JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 16