(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the vector equation a × x = b in R3, where a doesn't = 0. Show that:

(a) a · b = 0

(b) x = (b × a / ||a||^2) + ka is a solution to the equation, for any scalar k

2. Relevant equations

I'm not really sure, but I've been messing with these:

1. u x (v x w) = (u · w)v - (u · v)w

2. v x w = v2w3 - v3w2, v3w1 - v1w3, v1w2 - v2w1

3. The attempt at a solution

(a) for a · b = 0, b must = 0 since a can't = 0. for b = 0, x must = 0 since a can't = 0.

(b) i'm really lost!

x = ((a x X) x a / (a · a)) + ka

I have no idea if I'm headed in the right direction or where to go with this. Even a few hints would be greatly appreciated!

Thanks!

Tina

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Cross Products

**Physics Forums | Science Articles, Homework Help, Discussion**