Addition & Subtraction of Vectors question from MHT CET 2025 (21 Apr, Shift 1)

Answer: (c)

1. Three vectors form a triangle only if one of them equals the sum (or difference) of the other two, i.e. $\vec{A} \pm \vec{B} \pm \vec{C} = 0$ for some signs.
2. $\vec{B} + \vec{C} = 3\hat{i} - 4\hat{j} + 9\hat{k} \neq \vec{A}$; $\vec{A} - \vec{B} = 2\hat{i} + \hat{j} - 4\hat{k} \neq \vec{C}$; $\vec{A} + \vec{C} = 5\hat{i} - 3\hat{j} + 5\hat{k} \neq \vec{B}$.
3. No combination gives zero, so the vectors do not close into a triangle.
4. So the answer is (c) no triangle.