Physics, asked by rohan9570, 9 months ago

plizz solve this question it is from vector ​

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Answered by BrainlyTornado
1

QUESTION:

From the diagram of vectors arranged as shown in attachment 3, the correct relation among the vectors shown will be

ANSWER:

  • All the three are correct.

GIVEN:

 \vec{a} +  \vec{b}  +  \vec{e} = 0

 \vec{c}  -   \vec{d}  =   - \vec{a}

 \vec{b}+\vec{e} -\vec{c} = -\vec{d}

TO CHECK:

  • The given relations.

EXPLANATION:

Let us take the first case[ REFER ATTACHMENT 1 ]

 \vec{a} +  \vec{b}  +  \vec{e} = 0

All the three vectors are in same direction.

So we can take any two vectors.

Let \ us \  take  \  \vec{a} \ and \  \vec{b}

Resultant of these two vectors will be in the direction opposite to that of e vector.

 \vec{a} +  \vec{b} =  -  \vec{e}

Let us bring e vector to the left

 \vec{a} +  \vec{b}  +  \vec{e} = 0

Hence option 1 is correct.

Let us take the second case

[ REFER ATTACHMENT 2 ]

 \vec{c}  -   \vec{d}  =   -   \vec{a}

Let us reverse the direction of d vector. Then three vectors will be connected as head to tail. So the resultant of three vectors will be zero.

\vec{c} -  \vec{d} +  \vec{a} =  0

Take a vector to the right.

\vec{c} -  \vec{d}  =  -   \vec{a}

Hence option 2 is correct.

Let us take the third case [REFER ATTACHMENT 3 ]

 \vec{b}   +   \vec{e} -   \vec{c}  =  -  \vec{d}

We already know that

 \vec{a} +  \vec{b}  +  \vec{e} = 0

Rewrite the vectors for our convinience.

 \vec{b}  +  \vec{e} +  \vec{a}  = 0

We also know that

\vec{c} -  \vec{d}  =  -   \vec{a}

Multiply by minus sign on both sides.

\vec{a} =  \vec{d} - \vec{c}

Substitute value of a vector.

 \vec{b}  +  \vec{e}  + \vec{d} - \vec{c}  = 0

Take d vector to the right

 \vec{b}  +  \vec{e}   - \vec{c}  = -  \vec{d}

Hence option 3 is correct.

HENCE ALL THE THREE ARE SATISFIED.

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