1. ## proof

(iii) If
u × v = v × u then we must have u × v = 0.

(iv) If
u is a vector such that u × v = 0 for every vector v, then we must have u = 0.

2. Originally Posted by maths_123

(iii) If
[LEFT]u × v = v × u then we must have u × v = 0.

hint: note that the cross-product is anti-commutative. so in general, u x v = -v x u

(iv) If
u is a vector such that u × v = 0 for every vector v, then we must have u = 0.
i guess you could do this using the formula. the other thing i had in mind might not work. let $\bold{u} = \left< u_1,u_2,u_3 \right>$ and $\bold{v} = \left< v_1,v_2,v_3 \right>$

then $\bold{u} \times \bold{v} = \cdots = 0$

show that you must have $u_1 = u_2 = u_3 = 0$

3. I don't understand how u x v = -v x u is linked with

u × v = v × u then we must have u × v = 0.

And what forumal should i use?

4. Originally Posted by maths_123
I don't understand how u x v = -v x u is linked with

u × v = v × u then we must have u × v = 0.

And what forumal should i use?

u x v = -v x u

and

u x v = v x u

.
.
.

5. Originally Posted by Jhevon

u x v = -v x u

and

u x v = v x u

.
.
.
Thanks for the help, i was ablr to solve thw question after all