Finding a Vector

[nycmathguy]

Section 6.3

Please do 49 in step by step fashion. I will then do 48 and 50.

 

[MathLover1]

47.
given:
||v||=10
u=<-3,4>

first find the magnitude of vector u:

||u||=sqrt((-3)^2+4^2)=sqrt(9+16)=sqrt(25)=5

So the magnitude is 5. Compare that with magnitude of v (||v||=10). You see that the magnitude of u is 2 times smaller than the magnitude of v.
So to find vector v, we just multiply vector u by 2 and we get the following

v=<-3*2,4*2>
v=<-6,8>

 

[nycmathguy]

47.
given:
||v||=10
u=<-3,4>

first find the magnitude of vector u:

||u||=sqrt((-3)^2+4^2)=sqrt(9+16)=sqrt(25)=5

So the magnitude is 5. Compare that with magnitude of v (||v||=10). You see that the magnitude of u is 2 times smaller than the magnitude of v.
So to find vector v, we just multiply vector u by 2 and we get the following

v=<-3*2,4*2>
v=<-6,8>

 

[MathLover1]

correct

 

[nycmathguy]

correct

Very cool. I love learning new ideas. Back to precalculus on Friday, Saturday and Sunday.