Couuld someone please help me with the following proofs:
(iii) Ifu × 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.
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hint: note that the cross-product is anti-commutative. so in general, u x v = -v x u
(iv) Ifi guess you could do this using the formula. the other thing i had in mind might not work. let $\displaystyle \bold{u} = \left< u_1,u_2,u_3 \right>$ and $\displaystyle \bold{v} = \left< v_1,v_2,v_3 \right>$u is a vector such that u × v = 0 for every vector v, then we must have u = 0.
Need Help urgent please.
then $\displaystyle \bold{u} \times \bold{v} = \cdots = 0$
show that you must have $\displaystyle u_1 = u_2 = u_3 = 0$