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?

Printable View

- May 25th 2008, 02:34 PMa.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 PMTheEmptySet
if two vectors are colinear then the vectors are scalar multiples of each other

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

Then

$\displaystyle 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 PMa.a
this may be stupid but the 0 vector is (0,0,0)... rite?

- May 25th 2008, 02:58 PMReckoner