Question

If the order of two vectors $A$ and $B$ is reversed, then in the cross product of two vectors, the resultant vector

• A. changes only in direction
• B. changes only in magnitude
• C. changes in magnitude and direction
• D. do not change in both magnitude and direction

Answer 1

The correct option is A

changes only in direction

Explanation for correct option:

Step 1: Given data

The order of two vectors is reversed, we have to find how the magnitude or direction changes.

Step 2: Explanation

The cross product of A and B is given by $\overrightarrow{A}\times \overrightarrow{B}$.

If the order is reversed, the cross product becomes $\overrightarrow{B}\times \overrightarrow{A}$.

$$\begin{gathered} \overrightarrow{A}\times \overrightarrow{B}=AB\sin \theta \hat{n} \\ \overrightarrow{B}\times \overrightarrow{A}=AB\sin \theta (-\hat{n}) \end{gathered}$$

From the above equations, it is clear that the direction of $\overrightarrow{A}\times \overrightarrow{B}$ is opposite to the direction of $\overrightarrow{B}\times \overrightarrow{A}$ and their magnitudes are the same.

Therefore, they have different directions and the same magnitude.

The resultant vector changes only in direction.

Hence, option (A) is the correct option.