if a is a vector and |a|=3 and it makes equal angles with i,j and k then show that

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