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Math Help - [SOLVED] Vectors

  1. #1
    a.a
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    Question [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?
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    Quote Originally Posted by a.a View Post
    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} <br />
i && j && k \\<br />
a && b && c \\<br />
ta && tb && tc \\<br />
\end{vmatrix}= (b(tc)-c(tb)) \vec i - (a(tc)-c(tc)) \vec j +(a(tb)-b(ta)) \vec j= \vec 0
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  3. #3
    a.a
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    this may be stupid but the 0 vector is (0,0,0)... rite?
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    Quote Originally Posted by a.a View Post
    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).
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