Question

how a vector will affected if directions of its components be reversed?

Answer 1

Noting that reversing the direction of all components of a vector means multiplying the coefficient of every component by -1, this operation becomes a simple one to represent mathematically:

v⃗ =∑ni=1ciϕi→v⃗ ′=∑ni=1−ciϕiv→=∑i=1nciϕi→v→′=∑i=1n−ciϕi

where, of course, ϕ1,...,ϕnϕ1,...,ϕncomprise your chosen basis of dimension n and c1,...,cnc1,...,cnare the coefficients for those vectors.

It can become immediately clear what the result of this reversal is if you simply take out the negative sign from the summation representing v′v′ above.

v⃗ ′=∑ni=1−ciϕi=−∑ni=1ciϕi=−v⃗ v→′=∑i=1n−ciϕi=−∑i=1nciϕi=−v→

Thus, reversing the direction of all components of a vector simply gives you the negative of the original vector (which, of course, is the same thing as reversing the vector).

Answer 2

If the components of the vector reversed then it's direction will be change but there will be ni effect in magnitude.

Go through attachment...