Resultant of overrightarrow A + overrightarrow B is {overrightarrow R ₁}. On reversing vector over

English

Gujarati

Hindi

3-1.Vectors

medium

The resultant of $\overrightarrow A + \overrightarrow B $ is ${\overrightarrow R _1}.$ On reversing the vector $\overrightarrow {B,} $ the resultant becomes ${\overrightarrow R _2}.$ What is the value of $R_1^2 + R_2^2$

A

${A^2} + {B^2}$

B

${A^2} - {B^2}$

C

$2({A^2} + {B^2})$

D

$2({A^2} - {B^2})$

Solution

(c) ${\vec R_1} = \vec A + \vec B$, ${\vec R_2} = \vec A – \vec B$

$R_1^2 + R_2^2 = {\left( {\sqrt {{A^2} + {B^2}} } \right)^2} + {\left( {\sqrt {{A^2} + {B^2}} } \right)^2}$=$2\left( {{A^2} + {B^2}} \right)$

Standard 11

Physics

Share

Similar Questions

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $

medium

A body is at rest under the action of three forces, two of which are ${\vec F_1} = 4\hat i,\,{\vec F_2} = 6\hat j,$ the third force is

easy

Establish the following vector inequalities geometrically or otherwise:

$(a)$ $\quad| a + b | \leq| a |+| b |$

$(b)$ $\quad| a + b | \geq| a |-| b |$

$(c)$ $\quad| a – b | \leq| a |+| b |$

$(d)$ $\quad| a – b | \geq| a |-| b |$

When does the equality sign above apply?

medium

If the resultant of the two forces has a magnitude smaller than the magnitude of larger force, the two forces must be

easy

If $\vec{P}+\vec{Q}=\vec{P}-\vec{Q}$, then

easy