How do you find a unit vector that is perpendicular to both $-2i + j + 3k$ and $i - j - 2k$ ?

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Answer 1 · 2016-06-27T17:01:06

$hat e = {1/sqrt(3) hat i,-1/sqrt(3) hat j,1/sqrt(3) hat k}$

Given two vectors $vec u$ and $vec v$ , if they are linearly indepedend we can a unit vector perpendicular to both as follows.

$hat e = (vec u xx vec v)/norm(vec u xx vec v) = -(vec v xx vec u)/norm(vec u xx vec v)$

In the present case

${-2hat i, 1 hat j, 3 hat k}xx{1 hat i, -1 hat j, -2 hat k} = {1 hat i,-1 hat j,1 hat k}$

then

$hat e = {1/sqrt(3) hat i,-1/sqrt(3) hat j,1/sqrt(3) hat k}$

How do you find a unit vector that is perpendicular to both -2i + j + 3k-2i + j + 3k and i - j - 2ki - j - 2k?