Question

How do you find a vector of length 10 in the direction of v= <3,-2>?

Answer 1

Hello,

We are going to used the theorem of Thalès.

||v||=√(3²+(-2)²)=√13

k*√13=10==>k=10/√13

w=k.v=10/√13<3,-2>

Answer 2

Let x be the vector we seek. We recall the relationship of a vector to its length and direction:
dir x=x/|x|Because we art trying to find x from information on its length and direction, we rewrite this formula as,x=|x| dir x.We are given that |x|=13 We need to compute dir x from the information that x is in the same direction as ⟨1,−1⟩:dir x=dir ⟨3,−2⟩=⟨3,−2⟩|⟨3,−2⟩|.We need to compute the length |⟨3,−2⟩|. To do this, recall thatThe length of the vector y=⟨y1,y2⟩ is |y|=y21+y22−−−−−−√.Hence, |⟨3,−2⟩|=√13,.Thus
x=√13