Question

Given which of the following

Statements is not correct?

• A. $\overrightarrow { \mathrm { A } } , \overrightarrow { \mathrm { B } } , \overrightarrow { \mathrm { C } }$ and must each be a null vector
• B. The magnitude of $( \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { C } } )$ equals the magnitude of $( \vec { B } + \vec { D } )$
• C. The magnitude of $\vec { A }$ can never by greater than the sum of the magnitude of $\overrightarrow { \mathrm { B } } , \overrightarrow { \mathrm { C } }$ and $\overrightarrow { \mathrm { D } }$
• D. must lie in the plane of and if $\vec { A }$ and are not collinear and in the line of and , if they are collinear

Answer 1

Answer: (A)

$\overrightarrow { \mathrm { A } } , \overrightarrow { \mathrm { B } } , \overrightarrow { \mathrm { C } }$ and must each be a null vector

Answer 2

(1) The statement is not correct. It is because

can be zero in many ways other than

and beings each a null vector.

(2) The statement is correct as proved below.

$\therefore | \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { C } } | = | \overrightarrow { \mathrm { B } } + \overrightarrow { \mathrm { D } } |$

(3) The statement is correct as proved below

$\overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } + \overrightarrow { \mathrm { C } } + \overrightarrow { \mathrm { D } } = \overrightarrow { 0 }$ or $\overrightarrow { \mathrm { A } } = - ( \overrightarrow { \mathrm { B } } + \overrightarrow { \mathrm { C } } + \overrightarrow { \mathrm { D } } )$

(4) The statement is correct as proved below

$\overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } + \overrightarrow { \mathrm { C } } + \overrightarrow { \mathrm { D } } = \overrightarrow { 0 }$ or $\overrightarrow { \mathrm { A } } + ( \overrightarrow { \mathrm { B } } + \overrightarrow { \mathrm { C } } ) + \overrightarrow { \mathrm { D } } = \overrightarrow { 0 }$

The resultant sum of three vectors and can be zero only if () lies in the plane of and and these three vectors are represented by the three sides of a triangle taken in one order. If and $\vec { D }$ are collinear, then must be in the line of and $\vec { D }$ are collinear, then the vector sum of all the vectors will be zero.