Show that the diagonals are perpendicular using vectors

[Mr Davis 97]

I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular.

First, imagine that the sides of the equilateral parallelogram are the two vectors $\vec{A}$ and $\vec{B}$. Since the figure is equilateral, their magnitudes must be equal: $A = B$. Then $A^2 - B^2 = 0$. This can be factored using the dot product as $(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$. However, these two vectors are the diagonals of the parallelogram, and since their dot product is zero, they must be perpendicular.

Is this proof sufficient? Is there a better proof?

 

[blue_leaf77]

I would go with your proof.

 

[Mark44]

I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular.

First, imagine that the sides of the equilateral parallelogram are the two vectors $\vec{A}$ and $\vec{B}$. Since the figure is equilateral, their magnitudes must be equal: $A = B$. Then $A^2 - B^2 = 0$. This can be factored using the dot product as $(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$. However, these two vectors are the diagonals of the parallelogram, and since their dot product is zero, they must be perpendicular.

Is this proof sufficient? Is there a better proof?

You should be posting this and your other homework-type problems in the Homework & Coursework sections.