Applied Maths問題(Vector)

u = i - 2j + 4k

v = 2i - j - k

The vector perpendicular to both u and v, w

= u x v

=

│i j k│
│1 -2 4│
│2 -1 -1│

= 6i + 9j + 3k

The required unit vector is

= w / │w│

= (6i + 9j + 3k) / sqrt[(6)2 + (9)2 + (3)2]

= 1/sqrt(14) (2i + 3j + k)