Question

what would be the effect on a vector if all its components are reversed in direction?

PHYSICS ! Please help​

Answer 1

The direction of the vector will be reversed.

Explanation,

Let us suppose there is a vector say .

= ---eq(1)

Where is some component of the given vector .

Now, when the components are reversed, the new components will have the same magnitude as previous ones, but their direction will be rotated by 180°

The transformation will be as,

Now, the new vector formed ' will be,

' =

After taking the negative sign common, we will find some similarities with the above vector A.

' =

' = - [ from eq(1) ]

we conclude that the new vector has the same magnitude as the previous vector, but it is rotated by 180°.

Answer 2

The direction of the vector will be reversed.

Let us suppose there is a vector say N.

N =  $a_{1} + a_{2} + a_{3} ... + a_{n}$ ---eq(1)

Where $a_{i}$ is some component of the given vector .

Now, when the components are reversed, the new components will have the same magnitude as previous ones, but their direction will be rotated by 180°

The transformation will be as,

$a_{i}$ becomes  $-a_{i}$

Now, the new vector formed N' will be,

N' = $- a_{1} - a_{2} - a_{3} ... - a_{n}$

After taking the negative sign common, we will find some similarities with the above vector A.

N' = $- ( a_{1} + a_{2} + a_{3} ... + a_{n} )$

N' = -N [ from eq(1) ]

We conclude that the new vector has the same magnitude as the previous vector, but it is rotated by 180°.