Answer:
Yes, the paths of the two particles cross.
Location of path intersection = ( 1 , 2 , 3)
Explanation:
In order to find the point of intersection, we need to set both locations equal to one another. It should be noted however, that the time for each particle can vary as we are finding the point where the <u>paths</u> meet, not the point where the particles meet themselves.
So, we can name the time of the first particle , and the time of the second particle
.
Setting the locations equal, we get the following equations to solve for and
:
Equation 1
Equation 2
Equation 3
Solving these three equations simultaneously we get:
2 seconds
4 seconds
Since, we have an answer for when the trajectories cross, we know for a fact that they indeed do cross.
The point of crossing can be found by using the value of or
in the location matrices. Doing this for the first particle we get:
Location of path intersection = ( -1 + 2 , 4 - 2 , -1 + 2(2) )
Location of path intersection = ( 1 , 2 , 3)