if a is a vector and |a|=3 and it makes equal angles with i,j and k then show that
Asked by | 20th Feb, 2009, 05:33: PM
let a be a1 i + a2 j +a3 k
then given it makes equal angles with i,j,k axis
then a.i / |a| |i| = a.j/ |a| |j| =a.k / |a| |k|
we know that | i | = | j | = | k | =1
which implies a1=a2=a3
and also |a| = 3
i.e. a12+a22+a32 = 32
using a1 = a2 =a3 we get a1 = a2 =a3 = 3
now angle of a with i
cosθ = a.i/ |a| |i| = a1 / |a| = 1/ 3
hence proved
Answered by | 20th Feb, 2009, 09:31: PM
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