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Thread: find a vector perpendicular to both vector a and vector b

  1. #1
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    find a vector perpendicular to both vector a and vector b

    I did this one the way I did a previous problem like this but came up with a completely incorrect answer

    the question is:
    vector a = (2,1,0) and vector b = (-1,6,1) find a vector perpendicular to both.

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  2. #2
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    \displaystyle ||a\times b||=\begin{vmatrix}i&j&k\\2&1&0\\-1&6&1\end{vmatrix}=\mbox{normal vector}
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  3. #3
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    how about using dot product? haven't got to cross product yet
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  4. #4
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    The dot product produces a scalar not a vector.
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  5. #5
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    Quote Originally Posted by colorado View Post
    how about using dot product? haven't got to cross product yet
    Have you ever taking a determinant of a matrix?
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    You could use the dot product by setting up a system of two equations in three unknowns. That is, your unknown vector is r=(x,y,z). Set the dot product of r with both your initial vectors equal to zero, and solve the resulting system.
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    no, haven't gotten to that point
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  8. #8
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    Quote Originally Posted by Ackbeet View Post
    You could use the dot product by setting up a system of two equations in three unknowns. That is, your unknown vector is r=(x,y,z). Set the dot product of r with both your initial vectors equal to zero, and solve the resulting system.
    yeah, I tried that, thats how I've done it before, didn't work out. perhaps its time for a math break.
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  9. #9
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    Quote Originally Posted by colorado View Post
    yeah, I tried that, thats how I've done it before, didn't work out. perhaps its time for a math break.
    Please show what you did.

    To get a unique answer, you will need to impose a third condition on the vector you're trying to find (eg. you want it to be a unit vector).
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