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.

I have the following vectors $\vec b=\left(\begin{matrix}-4\\ 3 \end{matrix}\right)$ and $\left(\begin{matrix}x\\ y \end{matrix}\right)$

Now we know that the length of the x,y vector is 1, and that it has the same
direction as $\vec b$


The length teaches us $\sqrt{x^2+y^2}=1$

What does the direction teach us ?

share|improve this question
    
You can compute $x$ and $y$ from it. Rescaling the vector does not change the direction. So if you know that it has the same direction as $b$ and you know its length, then you get $x$ and $y$. –  fabee Jan 17 '13 at 10:14
    
When $(x,y)$ has the same direction as $\vec b$ then $(x,y)=\lambda \vec b$ for some $\lambda>0$ –  Christian Blatter Jan 17 '13 at 10:18
    
The direction teaches you the ratio, $y/x$. –  Gerry Myerson Jan 17 '13 at 11:12
    
It teaches you all you need to know about $\left(\begin{matrix}x\\ y \end{matrix}\right)$ namely that it is equal to $\vec b/5=\left(\begin{matrix}-4/5\\ 3/5 \end{matrix}\right)$. –  Tpofofn Jan 17 '13 at 11:38
add comment

1 Answer

asuueme $v=\left(\begin{matrix}x\\ y \end{matrix}\right)$ , $\sqrt{x^2+y^2}=r$ then $x=rsinp$ and $ y=rcosp$ p is angle respect to x axis that p determine direction of this vector let $v=\left(\begin{matrix}-4\\ 3 \end{matrix}\right)$ then p = $arctan\frac{3}{-4}$ and $\left(\begin{matrix}x\\ y \end{matrix}\right)$ has a same drection with $v=\left(\begin{matrix}-4\\ 3 \end{matrix}\right)$ then $arctan\frac{y}{x}=acctan\frac{3}{-4}$ that here$\left(\begin{matrix}x\\ y \end{matrix}\right)$ is unit vector

share|improve this answer
add comment

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.