Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

1) Given vectors $u = (1, 1, -2)$ and $v = (0, 1, 1)$, find the value of $t$ such that magnitude of $u + t(v)$ has the smallest value

I have no idea how to begin.

2) Given vectors $u = (1, 1, -2)$, $v = (0, 1, 1)$ and $w = (t, 2, -1)$ where $t$ is any real number. For what values of $t$ are there no scalars $x1, x2$ and $x3$ such that

$x1u + x2v + x3w = e_3$ where vector $e_3 = (0,0,1)$

I've set up

$[1 0 t;1 1 2;-2 1 -1]*[x1;x2;x3] = [0;0;1]$

and I get the sense that I'm supposed to reduce or solve the linear system to get a value for $t$ where there is no solution but am unable to proceed.

share|improve this question

1 Answer 1

Hint to begin : $||u + tv||^2 = ||u||^2 + 2t<u,v> + t^2||v||^2$ which is a polynomial in $t$.

share|improve this answer
    
How would I obtain 2t(u)(v)? I do not know how to perform such an operation. –  Kev Feb 15 '13 at 22:27
    
I also still do not see how this would help me. –  Kev Feb 15 '13 at 22:28

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.