The resultant of two vectors P and Q is R . When the direction of Q is reversed, the resultant is given by S . Which one of the following is true for vectors R and S ?

Correct answer: D. R^ 2 +S^ 2 =2 (P^ 2 +Q^ 2 ) (B) Given, P+Q=R After reversing direction of R , we gel array l r=-P-Q S=-P-Q array So let angle between P and Q be Q So resurtants. array l R^ 2 =p^ 2 +Q^ 2 +2 P Q θ...(1) s^ 2 =p^ 2 +Q^ 2 -2 P Q θ ...(2) \ array Adthing equation (1) and (2) R^ 2 +S^ 2 =2 (P^ 2 +Q^ 2 ) So, the corvect answer is R^ 2 +s^ 2 =2 (p^ 2 +Q^ 2 )

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

The resultant of two vectors P and Q is R . When the direction of Q...

The resultant of two vectors

\overrightarrow{\mathrm{P}}

and

\overrightarrow{\mathrm{Q}}

\overrightarrow{\mathrm{R}}

. When the direction of

\overrightarrow{\mathrm{Q}}

is reversed, the resultant is given by

\overrightarrow{\mathrm{S}}

. Which one of the following is true for vectors

\overrightarrow{\mathrm{R}}

and

\overrightarrow{\mathrm{S}}

Options

A $\mathrm{R}^{2}-\mathrm{S}^{2}= \left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)$
B $\mathrm{R}^{2}-\mathrm{S}^{2}=2(\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{Q}})$
C $\mathrm{R}^{2}+\mathrm{S}^{2}=4(\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{Q}})$
D $\mathrm{R}^{2}+\mathrm{S}^{2}=2 \left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)$

Correct answer

D. $\mathrm{R}^{2}+\mathrm{S}^{2}=2 \left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)$

Step-by-step solution

(B) Given,

P+Q=R

After reversing direction of

R

, we gel

\begin{array}{l} r=-P-Q \\ S=-P-Q \end{array}

So let angle between

P

and

Q

Q

So resurtants.

\begin{array}{l}R^{2}=p^{2}+Q^{2}+2 P Q \cos \theta...(1) \\ s^{2}=p^{2}+Q^{2}-2 P Q \cos \theta \quad...(2) \ \end{array}

Adthing equation (1) and (2)

R^{2}+S^{2}=2 \left(P^{2}+Q^{2}\right)

So, the corvect answer is $R^{2}+s^{2}=2 \left(p^{2}+Q^{2}\right)

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