Let a,b,c,k be rational numbers such that k is not perfect cube if ` a + b k^(3/2) + c k^(2/3) = 0` prove that ` a = b = c =0`

Let a,b,c,k be rational numbers such that k is not perfect cube if a + b k^(1/3) + c k^(2/3) = 0 prove that a = b = c =0

Let a,b,c, k be rational numbers such that k is not perfect cube if a+bk^((3)/(2))+ck^((2)/(3))=0 prove that a=b=c=0

If a = 3i - 2j + k, b = 2i - 4j - 3k, c = -i + 2j + 2k then a + b + c =

let a be unit vector, b = 2i + j - k and c = I + 3k. The maximum value of [a b c] is

Let a,b,c be real numbers with sum equals zero,let us denote (a^(k)+b^(k)+c^(k))/(k)=S_(k) then (S_(5)S_(2))/(S_(7)) is equal to :

If a = i - j + 2k, b = 2i + 3j + k, c = i - k , then magnitude of a + 2b-3c is