What type of result do you obtain when multiplying vectors A, B, and C in the order (AxB)xC?

What type of result do you obtain when multiplying vectors A, B, and C in the order (AxB)xC?

• A. Scalar
• B. Point
• C. A vector
• D. Matrix

Answer: (C)

When you multiply vectors A and B using the cross product, denoted as A × B, the result is another vector that is orthogonal (perpendicular) to both A and B. This outcome is fundamental to vector multiplication in three-dimensional space and is essential in understanding the behavior of vectors in physics. Next, when you take the resultant vector from the cross product (let's call it D = A × B) and then perform the cross product with vector C (i.e., D × C), you again get another vector. The properties of the cross product ensure that this new vector is also orthogonal to both D and C. Thus, the entire operation (A × B) × C yields a vector as a result. The correct answer is therefore that the final result is a vector.

When you multiply vectors A and B using the cross product, denoted as A × B, the result is another vector that is orthogonal (perpendicular) to both A and B. This outcome is fundamental to vector multiplication in three-dimensional space and is essential in understanding the behavior of vectors in physics.

Next, when you take the resultant vector from the cross product (let's call it D = A × B) and then perform the cross product with vector C (i.e., D × C), you again get another vector. The properties of the cross product ensure that this new vector is also orthogonal to both D and C.

Thus, the entire operation (A × B) × C yields a vector as a result. The correct answer is therefore that the final result is a vector.