Assertion A: "If the dot product and cross product of \(\vec{A}\) and \(\vec{B}\) are zero, it implies that one of the vectors \(\vec{A}\) and \(\vec{B}\) must be the null vector." Step 1: Understanding the Dot Product Condition The dot product of two vectors is given by: \[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos\theta \] If \(\vec{A} \cdot \vec{B} = 0\), then either: 1. One of the vectors is the null vector (\(\vec{0}\)), or 2. The vectors are perpendicular (\(\theta = 90^\circ\)). \[Step 2:\] Understanding the Cross Product Condition The cross product of two vectors is given by: \[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin\theta \, \hat{n} \] If \(\vec{A} \times \vec{B} = 0\), then either: 1. One of the vectors is the null vector (\(\vec{0}\)), or 2. The vectors are parallel (\(\theta = 0^\circ\) or \(180^\circ\)). \[Step 3\]: Combined Condition Analysis - If both the dot product and cross product are zero, the vectors must satisfy both conditions simultaneously. - This is only possible if at least one of the vectors is the null vector (\(\vec{0}\)), because a nonzero vector cannot be both parallel and perpendicular to another vector at the same time. Thus, Assertion A is true. --- Reason R: "Null vector is a vector with a zero magnitude." By definition, the null vector is a vector with zero magnitude, meaning: \[ |\vec{0}| = 0 \] This statement is correct. \[Step 4:\] Checking the Relationship Between A and R - Assertion A states that one of the vectors must be the null vector if both the dot product and cross product are zero. - Reason R defines the null vector correctly. Since Assertion A directly depends on the definition of the null vector (which is given in Reason R), R correctly explains A. Final Answer: \[ \boxed{A} \]