# How Is the Vector Solution 1/2(p-q) Derived?

• m00c0w
In summary, the conversation is about solving a problem involving triangles and vectors. The answer is 1/2(p-q) and one can express vector p in terms of PM and MQ. The relation between PM and MR is that they are the same distance. The equations used are: vec(MQ) + vec(PM) = vec(p) and vec(MQ) + vec(q) = vec(MR).
m00c0w
Hi I was wondering if anyone could help me with this problem:

http://img209.echo.cx/img209/5105/vector5mm.png

In my textbook it says the answer is 1/2(p-q) but I don't understand how that answer is acheived. Any help would be appreciated.

Many thanks.

Consider the triangle PMQ.Can u express $\vec{p}$ in terms of $\vec{PM}$ and $\vec{MQ}$...?

And the same for the other triangle...

What relation is there between $\vec{PM}$ and $\vec{MR}$ ?

Daniel.

In triangle PMQ $\vec{p}$ = $\vec{PM}$ + $\vec{MQ}$.

Also $\vec{PM}$ = $\vec{MR}$ as in they're the same distance. Could anyone explain how I get the answer please? As my test is now tomorrow

The way i see it

$$\left\{\begin{array}{c}\vec{MQ}+\vec{PM}=\vec{p}\\ \vec{MQ}+\vec{q}=\vec{MR} \end{array} \right$$

Daniel.

## 1. What is a vector problem?

A vector problem is a mathematical problem that involves the use of vectors, which are mathematical quantities that have both magnitude and direction. These problems often involve finding the sum, difference, or product of vectors.

## 2. What is 1/2(p-q) in relation to vector problems?

1/2(p-q) is a vector equation that represents the midpoint between two vectors, p and q. It is used in vector problems to find the average of two vectors or to find a vector that is equidistant from both p and q.

## 3. How do I solve a vector problem with 1/2(p-q)?

To solve a vector problem with 1/2(p-q), you first need to determine the values of p and q. Then, plug those values into the equation and perform the necessary operations (addition, subtraction, multiplication) to find the solution.

## 4. Can 1/2(p-q) be used for any type of vector problem?

No, 1/2(p-q) is specifically used for finding the midpoint between two vectors. It may not be applicable for other types of vector problems, such as finding the magnitude or direction of a vector.

## 5. Are there any tips for solving vector problems with 1/2(p-q)?

One tip for solving vector problems with 1/2(p-q) is to first draw a diagram or visualize the problem to better understand the relationship between the vectors. Additionally, make sure to carefully label and identify the vectors and their components before plugging them into the equation.

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