Question

Suppose that all sides of a quadrilateral are equal in legth and opposite sides are parallel. Use vector methods to show that the diagnoals are perpendicular.

Answer 1

(a.a)-(b.b)=|a|²-|b|²=0

As the dot product of the diagonals is 0, the diagonals must be perpendicular.

Explanation:

1. All the sides are equal in lengths and the sides that are opposite to each other and parallel so it can be expressed as the same vectors.
2. These diagonals can be expressed by equation a+b and a-b
3. Take the dot product of the diagonals and simplify.

(a+b).(a-b)=(a.a)-(b.b)

4. A vector dotted with itself is its length squared, and we know that the

side lengths are equal to each other.

(a.a)-(b.b)=|a|²-|b|²=0