1.
Given three vectors V⃗1=ai^+bj^+ck^\vec{V}_1 = a\hat{i} + b\hat{j} + c\hat{k}, V⃗2=bi^+cj^+ak^\vec{V}_2 = b\hat{i} + c\hat{j} + a\hat{k}, V⃗3=ci^+aj^+bk^\vec{V}_3 = c\hat{i} + a\hat{j} + b\hat{k}. In which one of the following conditions are V⃗1\vec{V}_1, V⃗2\vec{V}_2, V⃗3\vec{V}_3 linearly independent?