a and b are two unit vector mutually perpendicular. Find a unit vector equally inclined to a,b,a×b
Rivu , 5 Years ago
Grade 10
Vectors> a and b are two unit vector mutually perp...
1 Answers
Arun
Last Activity: 5 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
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