Three vectors $\vec{P}, \vec{Q}$ and $\vec{R}$ are shown in the figure. Let $S$ be any point on the vector $\vec{R}$. The distance between the points $P$ and $S$ is $b|\vec{R}|$. The general relation among vectors $\vec{P}, \vec{Q}$ and $\vec{S}$ is

(A) $\vec{S}=(1-b) \vec{P}+b \vec{Q}$

(B) $\vec{S}=(b-1) \vec{P}+b \vec{Q}$

(C) $\vec{S}=\left(1-b^{2}\right) \vec{P}+b \vec{Q}$

(D) $\vec{S}=(1-b) \vec{P}+b^{2} \vec{Q}$

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Vector

Three vectors

P, Q

and

R

are shown in the figure. Let

S

be any point on the vector

R

. The distance between the points

P

and

S

b ∣ R ∣

. The general relation among vectors

P, Q

and

S

Answer: (A)

Since

S

lies on

R

and

R = Q - P

, we have

S - P = b R = b (Q - P)

. Expanding:

S = P + b Q - b P = (1 - b) P + b Q

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Single correct option