Given three vectors
\( \mathrm{P} \)
\( \overrightarrow{\mathrm{V}}_{1}=\mathrm{a} \hat{i}+b \hat{\mathrm{j}}+\mathrm{ck}, \overrightarrow{\mathrm{V}}_{2}=\mathrm{bi}+\hat{\mathrm{c}}+\mathrm{ak} \),
W
\( \overrightarrow{\mathrm{V}}_{3}=c \hat{i}+\hat{a}+b \hat{k} \) in which one of the following
conditions \( \vec{V}_{1}, \vec{V}_{2} \) and \( \vec{V}_{3} \) are linearly independent?
(1) \( a+b+c=0 \) and \( a^{2}+b^{2}+c^{2} \neq a b+b c+c a \)
(2) \( a+b+c=0 \) and \( a^{2}+b^{2}+c^{2}=a b+b c+c a \)
(3) \( a+b+c \neq 0 \) and \( a^{2}+b^{2}+c^{2}=a b+b c+c a \)
(4) \( a+b+c \neq 0 \) and \( a^{2}+b^{2}+c^{2} \neq a b+b c+c a \)
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