Question

Find a scalar S such that ||v+Sw|| = 6 when v=<-2,5> and w=<3,-2>

Answer 1

|| <num1, num2, ...> || means sqrt( num1^2 + num2^2 + ...)

<-2, 5> + S<3, -2>
=<-2, 5> + <3S, -2S>
=<-2 + 3S, 5 -2S>

|| <-2 + 3S, 5 -2S> || = sqrt( (-2+3S)^2 + (5-2S)^2 )

We want sqrt( (-2+3S)^2 + (5-2S)^2 ) to equal 6. Following so far?

Answer 2

Yep!

Answer 3

Are you able to finish it?

Answer 4

No this is where I got stuck haha

Answer 5

Try squaring both sides.

Next you'll expand the squares.

And then just solve for S.

Answer 6

@FutureMathProfessor are you ok? you just asked how to solve sqrt(something) = something?

Answer 7

Matlab gives me: 347^(1/2)/13 + 16/13 and 16/13 - 347^(1/2)/13 :S

Maybe this is why it's so difficult? Let me check this by hand...

Answer 8

You end up with sqrt(13x^2 - 32x + 29) = 6 which definately doesn't come out to anything nice...