Minimum distance between two vectors on a graph?

[dan.g117]

Homework Statement

This is just a theoretical question so there aren't any values for the variables but there are two vectors with constant velocity. Given their velocity, magnitude, direction how can one calculate the minimum distance between the two vectors.

Also have to solve graphically

Homework Equations

The Attempt at a Solution

I'm currently under the assumption it has to do with slope or something along those lines.
Input greatly appreciated.

http://img22.imageshack.us/my.php?image=examplehr3.jpg

thanks!

 

[LowlyPion]

Welcome to PF.

Algebraically you can take the position difference vector as a function of time and determine the minimum.

Graphically ... just extending the line of action of position vectors doesn't seem to solve the problem you are asking about minimizing the position difference vector. A position graph alone doesn't really account for the rate of change of position as a function of time.

 

[nlightner]

I can provide some insights into the problem and possible approaches to solving it. The minimum distance between two vectors on a graph can be calculated using the concept of vector projection. This involves finding the component of one vector that lies in the direction of the other vector, and then calculating the distance between the two vectors using this component.

To solve graphically, you can plot the two vectors on a graph and draw a line connecting the two vectors. This line represents the shortest distance between the two vectors. You can then use the Pythagorean theorem to calculate the length of this line, which is the minimum distance between the two vectors.

Another approach is to use vector algebra to calculate the dot product between the two vectors. The dot product represents the magnitude of one vector in the direction of the other vector. By dividing this value by the magnitude of the second vector, you can calculate the length of the component of the first vector in the direction of the second vector. This component can then be used to calculate the minimum distance between the two vectors.

Overall, the minimum distance between two vectors on a graph can be calculated using a combination of vector projection, Pythagorean theorem, and vector algebra. It is important to note that the values of velocity, magnitude, and direction are crucial in accurately calculating the minimum distance. Therefore, it is important to have these values in order to solve the problem effectively.