Which statement is always true for the cross product $\mathbf{A}\times\mathbf{B}$?
AIt is a scalar equal to $A_1B_1+A_2B_2+A_3B_3$
BIt is a vector perpendicular to both $\mathbf{A}$ and $\mathbf{B}$
CIt is parallel to both $\mathbf{A}$ and $\mathbf{B}$
DIts value is unchanged when $\mathbf{A}$ and $\mathbf{B}$ are interchanged
Answer & Solution
Correct answer: B. It is a vector perpendicular to both $\mathbf{A}$ and $\mathbf{B}$
The cross product gives a vector normal to both original vectors. Interchanging the vectors changes the sign: $\mathbf{A}\times\mathbf{B}=-(\mathbf{B}\times\mathbf{A})$, so option D is false.
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