Question

Let u= (2,-1), v=(-2,4) and w=(-5,7).
Decide s and t so that the vector su+tv is twice as long as vector w but in an oppsite direction.

Answer 1

I've gotten somewhere (I think).
su+tv=(2s-5t;7t-s)
But how do we get to know the coordinates of (the twice as long and oppositely directed) w?

Answer 2

I'm so terrible at vector geometry it's starting to get embarassing. :c

Answer 3

first find w when it is twice longer but in opposite way so thats just -2w=(10,-14). the norm of this will be two times the norm of w and is in the opposite direction... so we find s and t if
su+tv=-2w
s(2,-1)+t(-2,4)=(10,-14)

so we'll solve the following system of equation:
2s-2t=10
-s+4t=-14
solving this we'll have
s=2
t=-3

Answer 4

@Noliec don't be :D I bet you have your own field of experty in mathematics

Answer 5

Really, you're just able to -2*w and get a twice as (oppositely directed) long vector? Buhuhu me, thanks!

Answer 6

x_x

Answer 7

Yes.

Answer 8

Embarassed for calling you over here @FoolForMath, sorry!

Answer 9

yes first we set this to opposite direction so -w, then we know that it must be two times so I multiplied it to 2 to get twice as long as that. so the norm of this vector will be sqrt(269)=2sqrt(74) which is 2 times the length of w which is sqrt(74)

Answer 10

No problem :)

Read here: http://www.britannica.com/EBchecked/topic/624306/vector

Answer 11

Moreover, my favorable area would be (non-geometry) analysis and general proofs.

Answer 12

I shall read.