Thread: Vector proofs urgent help needed

For each of the following statements, determine whether it is true or false. If the statement is true then prove it; if it is false then give an example where the statement fails to hold.

(i) If

u, v,w is a right-handed triple of vectors, with u orthogonal to v, then v must be orthogonal to w.

(ii) (u × v) × w = u × (v × w) for all vectors u, v,w.

(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.


can some one help me asap i dnt knw wer 2 start .

Originally Posted by omarj

For each of the following statements, determine whether it is true or false. If the statement is true then prove it; if it is false then give an example where the statement fails to hold.

(i) If

u, v,w is a right-handed triple of vectors, with u orthogonal to v, then v must be orthogonal to w.

What is the DEFINITION of "right-handed triple" of vectors?

(ii) (

u × v) × w = u × (v × w) for all vectors u, v,w.

Surely at the time you learned about the cross product you learned the fact, if not the proof, that u x v is associative. What does that mean?

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

[/quote]
The cross product, u x v, is anti-symmetric. What does that mean?

(iv) If

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


can some one help me asap i dnt knw wer 2 start .

One definition of cross prioduct u x v is that it is the vector that is perpendicular to both u and v (in the "right-hand" sense) with length equal to . Since this says u x v= 0 for every vector v, try taking v to be a vector that is perpendicular to u and has length 1. What is the length of |u x v|?

thanks that helped alot