# [SOLVED] Vectors

• May 25th 2008, 02:34 PM
a.a
[SOLVED] Vectors
Using components show that vector u cross vector v = the 0 vector if u and v are collinear.

What does the fact that u and v are colinear tell us?
• May 25th 2008, 02:53 PM
TheEmptySet
Quote:

Originally Posted by a.a
Using components show that vector u cross vector v = the 0 vector if u and v are collinear.

What does the fact that u and v are colinear tell us?

if two vectors are colinear then the vectors are scalar multiples of each other

let $u =(a,b,c)$ and $v= t\cdot u =(ta,tb,tc), t\ne 0$
Then

$u \times v = \begin{vmatrix}
i && j && k \\
a && b && c \\
ta && tb && tc \\
\end{vmatrix}= (b(tc)-c(tb)) \vec i - (a(tc)-c(tc)) \vec j +(a(tb)-b(ta)) \vec j= \vec 0$
• May 25th 2008, 02:55 PM
a.a
this may be stupid but the 0 vector is (0,0,0)... rite?
• May 25th 2008, 02:58 PM
Reckoner
Quote:

Originally Posted by a.a
this may be stupid but the 0 vector is (0,0,0)... rite?

Yes. In $\mathbb{R}^3$, the zero vector is indeed $\left(0,\;0,\;0\right)$.