How to Prove Vector Identity k = (a+b)(c+d)?

[colerelm1]

Homework Statement

The following are all vectors:
a, b, c, d

k = (a+b) (c+d)

prove: k = (a x c) + (a x d) + (b x c) + (b x d)

Homework Equations

The Attempt at a Solution

I have tried to start it by doing:

|a| = a = sqrt(a_x^2 + a_y^2)

is that a correct start at it? I really am pretty lost...

 

[JaredJames]

As per my other post, do you understand how to expand the brackets to get between the two solutions for k?

Jared

 

[colerelm1]

I guess I don't...Could you please explain?

 

[JaredJames]

Have a read through this:

http://richardbowles.tripod.com/maths/algebra/brackets.htm

It will show you how to expand the brackets.

 

[colerelm1]

Oh, yeah I know how to do that but what if what I meant by "k = (a+b) (c+d)" was actually the dot product of k = (a+b) (c+d) instead of just k = (a+b) x (c+d)? Does that make a difference?

 

[JaredJames]

k = (a+b)(c+d) = (a+b)x(c+d) = (a x c)+(a x d)+(b x c)+(b x d)

What you have there is expanding the brackets, this is not the dot product.

The dot product of [a,b][c,d] = ac + bd.

The question shows bracket expansion not dot product. So yes, there is a difference, particularly in notation (dot product = square brackets with commas seperating vectors, expansion = round brackets with standard mathematical operators).