# Thread: Problem

1. ## Problem

Demonstrate , using the definition of the dot product, that the length of the vectors a and b are equal if an only if the diagonals of the quadrilateral OAQB are orthogonal.

A Q

O B

its meant to be a rhombus

Hint: Use that if (OA-OB) is perependicualr to (OA+OB) then OA = OB and vice versa.

P.S dont tell me the answer just need some help of what to do help much appreciated

2. please help i need to do this a.s.a.p

3. Originally Posted by adam_leeds
Demonstrate , using the definition of the dot product, that the length of the vectors a and b are equal if an only if the diagonals of the quadrilateral OAQB are orthogonal.
Take O as the origin, A as the point with position vector a, B as the point with position vector b. Then Q has position vector a + b. The vector from B to A is a - b, and the condition for these two vectors to be perpendicular is (a + b).(a - b) = 0.

4. Originally Posted by Opalg
Take O as the origin, A as the point with position vector a, B as the point with position vector b. Then Q has position vector a + b. The vector from B to A is a - b, and the condition for these two vectors to be perpendicular is (a + b).(a - b) = 0.
thanks for the help