vector cal question?

Question

find a vector with magnitude sqrt(10) in the direction of v = <-1,1>.

How am i supposed to solve this problem? please be detailistic with your answers.

I was just thinking of multiplying them together, would that be right?

Answer 1

The easiest way to do this is first to make <-1,1> a unit vector, this is done by multiplying it by its magnitude's inverse (=Sqrt(2)) so you get vector <-Sqrt(2), Sqrt(2)> then multiply by the magnitude Sqrt(10)<-Sqrt(2),Sqrt(2)>=<-2Sqrt(5),2Sqrt(5)> and this vector has the desired magnitude.

Answer 2

First calculate the magnitude of v.

|| v || = √[(-1)² + 1²] = √(1 + 1) = √2

But you want the magnitude to be √10. So multiply the vector by the factor √10/√2 = √(10/2) = √5

The desired vector is:

(√5)v = (√5)<-1, 1> = <-√5, √5>