Find the vector x in the opposite direction of a vector such that the length of x equals a certain number?

Question

Can you explain to me how to solve a problem such as this?
Find the vector x in the opposite direction of a GIVEN vector u such that the length of the original vector x equals a certain GIVEN number?
Thanks.

Answer 1

To reverse the direction of a vector, change the sign of each component.

Suppose a given vector is and you want to change its length so the new vector has length L. Simply multiply each component by L/sqrt(a^2 + b^2 + c^2).

Answer 2

you come across a unit vector interior the comparable direction as "v" via dividing the upload-ons with the help of the fee; IvI = Sqrt(9+4) = Sqrt(13) parallel unit vector = v/IvI = <(3/Sqrt(13), -2/Sqrt(13)> Then multiply with the aid of way of -a million to discover the unit vector opposite "v"; antiparallel unit vector = -v/IvI = <-3/Sqrt(13), 2/Sqrt(13)>