SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

Show |a|b + |b|a is orthogonal to |a|b-|b|a . Do not assume 2 or 3 dimensional vectors.
So I tried using the dot product, but I just end up with some magnitude minus another = 0, in which case, I still have no idea what to do...

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

It's pretty simple, same as the last time you asked. You have an expression for each of the vectors, dot them together. You will find that you have four terms in the expansion because it's the FOIL rule (as you might have been taught). You know, (x + y)(x - y) = x^2 + xy - xy - y^2. It's the antisymmetric one. So you get that, do some simplification, and it could be that it comes out to zero. If you remember that any two vectors whose dot product is zero are orthogonal to each other, well, you've solved it!

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

well I didn't know that |a|b dot |a|b = |a|^2 |b|^2, based on one of the properties of dot product, but thanks anyway!

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

It probably makes sense, geometrically.