Consider a rectangle with vertices at E,F,G and H.

Question

Consider a rectangle with vertices at E, F, G and H. Suppose $\overrightarrow{EF}$ = p and $\overrightarrow{FG}$ = q. Express each of the vectors EH, GH, FH and GE in terms of p and q.

Hi everybody. I've spend a day or two trying to solve this coursework question that I was given. I drew a rectangle and added the vertices and I tried to use the method that was explained during class, but I couldn't get my head round it. I've had several failed attempts at this writing it out and searching the internet for any other ways that I might be able to figure it out, but what I've seen so far still doesn't help me understand how to solve the problem.

Any help in any way would be much appricated.

Answer 1

Consider the figure below:

Hints:

1. Two vectors are equal if they have the same magnitude and direction. What vector has the same magnitude and direction as $\overrightarrow{EF}$? as $\overrightarrow{FG}$?
2. Opposite vectors have the same magnitude and opposite directions. What vector is opposite to $\overrightarrow{HG}$?
3. The parallelogram rule states that the sum $\boldsymbol{u} + \boldsymbol{v}$ of two vectors $\boldsymbol{u}$ and $\boldsymbol{v}$ is found by placing the tail of vector $\boldsymbol{v}$ at the head of vector $\boldsymbol{u}$, then drawing the vector from the tail of vector $\boldsymbol{u}$ to the head of vector $\boldsymbol{v}$. What vector is the sum of $\overrightarrow{FG}$ and $\overrightarrow{GH}$?
4. The difference $\boldsymbol{u} - \boldsymbol{v}$ of two vectors $\boldsymbol{u}$ and $\boldsymbol{v}$ is found by placing the tail of vectors $\boldsymbol{u}$ and $\boldsymbol{v}$ at the same point, then drawing the vector from head of vector $\boldsymbol{v}$ to the tail of vector $\boldsymbol{u}$. What vector is the difference of $\overrightarrow{EF}$ and $\overrightarrow{FH}$?