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

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

Grade:10

1 Answers

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

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