Question

plizz solve this question it is from vector ​

Answer 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.