The two vectors A and B are drawn from a common point and C = A + B...

We are given: (\vec{C}=\vec{A}+\vec{B}) Taking magnitude squared: (C^2=A^2+B^2+2 A B \cos \theta) where (\theta) is the angle between (\vec{A}) and (\vec{B}). Case Analysis: 1. If $C^2=A^2+B^2$ : (2 A B \cos \theta=0 \quad \Rightarrow \quad \cos \theta=0 \quad \Rightarrow \theta=90^{\circ}) (\checkmark) Statement (1) is correct. 2. If $C^2 < A^2+B^2$ : (2 A B \cos \theta < 0 \Rightarrow \cos \theta < 0 \Rightarrow \theta > 90^{\circ}) (\checkmark) Statement (2) is correct. 3. If $C^2 > A^2+B^2$ : (2 A B \cos \theta > 0 \Rightarrow \cos \theta > 0 \Rightarrow \theta < 90^{\circ}) So angle is less than (90^{\circ}), not greater. X Statement (3) is incorrect. (\checkmark) Statement (4) is correct.