Question

Find a unit vector which is perpendicular to both the vectors 2 i^+j^-k^and 3i^+4j^-k.

Answer 1

The vector obtained from their cross product will be mutually perpendicular to them:

z=i x j

$z=((+1)(-1)-(-1)(+4))i+((-1)(3)-(+2)(-1))j+((+2)(+4)-(+3)(+1))k\\z=((-1)-(-4))i+((-3)-(-2))j+((8)-(3))k\\z=(3)i+(-1)j+(5)k\\z=3i-j+5k$