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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's assume a helicopter crashes into a wall after flying in a straight line:

$$g : \overrightarrow {OX} = \begin{pmatrix}2\\5\\28 \end{pmatrix}+ \lambda*\begin{pmatrix}1\\\frac{1}{3}\\\frac{-1}{11} \end{pmatrix} $$

There are four walls which form a valley (it is formed by $1$,$2$; $2,3$; $3,4$ and$ 4,1$): $$\epsilon_1 : 9922x+6716y+539z = 95033 $$ $$\epsilon_2 : 20314x-6708y+4543z = 262821 $$ $$\epsilon_3 : 67179x+7766y+12803z = 4737245606 $$ $$\epsilon_4 : 15414x+135576y+22540z = 1213884 $$

How can I determine in which of the these planes the helicopter crashes? I was able to calculate four different $\lambda$ (after substituting $g$ into $\epsilon$) and the four intersection points. I understand why there are four intersection points since the planes have an infinity x,y,z range and as long as the line is not parallel there will always be an intersection point...

But there has to be a way to determine the actual wall.

share|cite|improve this question
up vote 0 down vote accepted

Calculate the lambdas for each of the planes so that the helicopter intersects the particular plane (I guess lambda would be infinity if the helicopter is going parallel to the plane), and choose the "earliest" (i.e. smallest positive) lambda. The associated plane must be the one the helicopter crashes into.

share|cite|improve this answer

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.