- #1

- 8

- 0

## Homework Statement

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

## Homework 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

## 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

Last edited: