Thread: Parallelogram and Vectors

A Parallelogram with sides of equal length is called a rhombus. Show that the diagonals of a rhombus are perpendicular.

So, I start with v and u which are perpendicular vectors. v + w is a diagonal of the rhombus.

I am not sure how to get the other one, or to solve this question, really.

I know that in order for two vectors to be perpendicular then the dot product must be 0.

so I guess, I need both diagonals and to see if their dot product is zero?

Originally Posted by zodiacbrave

A Parallelogram with sides of equal length is called a rhombus. Show that the diagonals of a rhombus are perpendicular.

Suppose that are adjacent sides of thee rhombus.
Then the diagonals are .
Now look at the dot product,

Thank you for your reply..

I know (a + b) is just a regular vector but the fact that we are labeling it as the sum of two other vectors is confusing to me. What I mean is, if vector a has components (a1, a2) and vector b has components (b1, b2) then won't the dot product of (a + b) and (a - b)
equal (a1)^2 - (b1)^2 + (a2)^2 - (b2)^2

I guess, I am not understanding the actual method of proving it algebraically.

Originally Posted by zodiacbrave

I know (a + b) is just a regular vector but the fact that we are labeling it as the sum of two other vectors is confusing to me. What I mean is, if vector a has components (a1, a2) and vector b has components (b1, b2) then won't the dot product of (a + b) and (a - b)
equal (a1)^2 - (b1)^2 + (a2)^2 - (b2)^2

Recall that