How do you find a unit vector perpendicular to both vector u(1, -1,-1)and vector v(2, -2, 3)?

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Answer 1 · 2016-07-11T07:44:33

#+-(1/sqrt 2, 1/sqrt 2, 0)#

The vector perpendicular to both #u and v# is #+-(uXv)/|uXv|#

#=+-((1. -1, -1)X(2, -2, 3))/|(1. -1, -1)X(2, -2, 3)|#

Now, the numerator vector is

#((-1)(3)-(-1)(-2), (-1)(2)-(1)(3), (1)(-2)-(-1)(2))#

#=+-(-5, -5, 0)# and #|(-5, -5, 0)|=5 sqrt 2#'

So, the answer is #+-#(-5, -5, 0)#/(5 sqrt 2)#

#=+-(1/sqrt 2, 1/sqrt 2, 0)#.