Purchase Solution

Vectors : Identities and Dot Products

Not what you're looking for?

Ask Custom Question

How could you use the properties of the dot product to prove the following identities: (where u and v denote vectors in Rn)

a) ||u + v||^2 + ||u-v||^2 = 2(||u||^2 + ||v||^2)
b) ||u + v||^2 - ||u-v||^2 = 4u dot v

Note:
dot = dot product
^ = power
||= distance.

Purchase this Solution

Solution Summary

The properties of the dot product are used to prove the vector identities.

Solution Preview

a)
||u + v||^2= (u+v, u+v) where ( , ) shows the inner product (i.e. dot product). Then we have:

||u + v||^2= (u+v, u+v)= (u, u)+ (u, v)+ (v, u)+ (v, ...

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.