Originally Posted by

**Ideasman** I have to find two unit vectors that are parallel to

<3, 1, 2>

And then I have to write each vector as the product of its magnitude and a unit vector.

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My approach:

We know that two vectors are parallel if their cross product is equal to 0.

<math>\mathbf{a} \times \mathbf{b} = \mathbf{A}_{\times} \mathbf{b} = \begin{bmatrix}0&-a_3&a_2\\a_3&0&-a_1\\-a_2&a_1&0\end{bmatrix}\begin{bmatrix}b_1\\b_2\\b_3 \end{bmatrix}</math>

Using the above, I plugged in a_1, b_1, c_1 and then augmented it with the 0 vector, but I just ended up with a_1 = 0, b_1 = 0, and c_1 = 0 which wasn't very helpful. Any ideas?

*EDIT* I guess Wikipedia math code doesn't conform to this site;

It's mean to be:

a x b = [[0, -a_3 a_2], [a_3, 0, -a_1], [-a_2, a_1, 0]] multiplied with the vector [b_1, b_2, b_3]; of course there is also the determinant method.