Question

The angle between \( \vec{A} \times \vec{B} \) and \( \vec{B} \times \vec{A} \) is:

• A. \( 90^\circ \)
• B. \( 60^\circ \)
• C. \( 180^\circ \)
• D. \( 0^\circ \)
• E. \( 270^\circ \)

Hint:

Whenever you encounter the cross product of two vectors, remember the anti-commutative property: \( \vec{A} \times \vec{B} = - (\vec{B} \times \vec{A}) \). This property helps in determining the direction and angle between the cross products.

Answer 1

The Correct Option is C

We are asked to find the angle between the vectors \( \vec{A} \times \vec{B} \) and \( \vec{B} \times \vec{A} \). First, recall that the cross product is anti-commutative, meaning that: \[ \vec{B} \times \vec{A} = - (\vec{A} \times \vec{B}) \] So, the two vectors \( \vec{A} \times \vec{B} \) and \( \vec{B} \times \vec{A} \) are opposites of each other. Therefore, the angle between them is \( 180^\circ \), as they are in exactly opposite directions.
Thus, the correct answer is option (C), \( 180^\circ \).