Thread: Vectors problem

a and b are two position vectors of two distinct points A and B , neither of which is the origin. show that if (modulus) a+b = (modulus) a-b , then a is perpendicular to b using :
a. a vector algebraic method
b. a geometric argument
I don't quite understand what they mean by these^
I've drawn a quick diagram using word, see image below.

Originally Posted by kandyfloss

a and b are two position vectors of two distinct points A and B , neither of which is the origin. show that if (modulus) a+b = (modulus) a-b , then a is perpendicular to b using :
a. a vector algebraic method
b. a geometric argument

For part a), recall that .

For part b), what type of quadrilateral diagonals of equal lengths?

part a) oh yeah, i agree on that rule. but how does it help me explain a is perpendicular to b?
part b) parallelogram ?

Originally Posted by kandyfloss

part a) oh yeah, i agree on that rule. but how does it help me explain a is perpendicular to b?
part b) parallelogram ?

You are given that squaring we get
.
Expand to see what happens.

Ok, thanks. and about the part b) since it's a parallelogram the diagonals intersect at 90 deg and adjacent sides are perpendicular to each other. right?