Find the unit vector?

Question

If a= i-j+2k and b=2i+3j-k

Find a unit vector perpendicular to both a and b.

If anyone could show me the steps involved or some hints, that would be great. Thanks!

Answer 1

Calculate the unit vector perpendicular to both a and b:

n=(a*b)/|a*b|

  =(i-j+2k)*(2i+3j-k)/|(i-j+2k)*(2i+3j-k)|

  =(-5i+5j+5k)/|-5i+5j+5k|

  =(-5i+5j+5k)/(sqrt 75)

  =(-5i+5j+5k)/5(sqrt 3)

  =(-i+j+k)/(sqrt 3)

Therefore, the unit vector perpendicular to both a and b is (-i+j+k)/(sqrt 3)