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Math Help - Vector cross products of vectors with unique directions.

  1. #1
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    Vector cross products of vectors with unique directions.

    Suppose we have vectors v1,v2,v3,v4 whose directions are unique. We take the cross product of v1 and v2 which gives us a vector that is not in the direction of v3. If we cross this vector with v3, we will get another vector (call it v5). Will v5 not be in the direction of v1,v2, and v3? Suppose we cross v5 with v4 (whose direction is not the same as v5), will we get a vector (call it v6) whose direction is perpendicular to v1,v2,v3,v4, and v5?
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  2. #2
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    Re: Vector cross products of vectors with unique directions.

    You can have v_5 in the same direction as v_1 or v_2. All you know is that it's perpendicular to v_1\times v_2 and v_3. Then v_6=v_5  \times v_4 is perpendicular to v_5 and v_4, but we don't know about v_1, v_2, and v_3.

    If a vector w_1 is perpendicular to w_2, and w_2 is perpendicular to w_3, that doesn't mean that w_1 is perpendicular to w_3.

    If you're confused by all this, try working out an example - say v_1=i, v_2=j, v_3=i+j, and v_4=k.

    - Hollywood
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