# a and b are two unit vector mutually perpendicular. Find a unit vector equally inclined to a,b,a×b

Arun
25758 Points
3 years ago

we have c =xa + yb +z (a x b)
c.a = x
and
c.b = y
hence x = y = cos theta

now c.c = c^2
(xa + yb +z (a x b)).(xa + yb +z (a x b)) =  |c|^2

2 x^2 +z^2 |a|^2 |b|^2 – (a.b)^2 = 1
2 x^2 + z^2 – 0 = 1
since a and b are perpendicular to each other

hence z^2  = 1 – 2x^2 = 1- 2 cos^2theta = – cos 2$\theta$