if a, b, c are mutually perpendicular unit vectors then find the value of [a b c]²
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Consider a,b,c as complex numbers which can be represented in the cartesian plane similar to vectors.
Let a=cosx + i sinx
b=cosy + i siny
c=cosz + i sinz
all the above complex numbers have modulus 1.
since a+b+c=0
hence sigma(cosx) + i sigma(sinx)=0
hence real and imaginary both parts are separately zero.
a^2+b^2+c^2=cos2x + cos2y + cos2z+ i(sin2x + sin2y + sin2z)=0
expand (a+b+c)^2=0 to get the result
Let a=cosx + i sinx
b=cosy + i siny
c=cosz + i sinz
all the above complex numbers have modulus 1.
since a+b+c=0
hence sigma(cosx) + i sigma(sinx)=0
hence real and imaginary both parts are separately zero.
a^2+b^2+c^2=cos2x + cos2y + cos2z+ i(sin2x + sin2y + sin2z)=0
expand (a+b+c)^2=0 to get the result
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