Understanding Cross Product of Vectors

What is the significance of the order in the cross product of two vectors?

• The order does not matter.

• The order determines the magnitude.

• The order affects the direction of the resulting vector.

• The order changes the vectors involved.

How are the components of vectors arranged in the matrix method for finding the cross product?

• In a 2x2 matrix.

• In a single row.

• In a 3x3 matrix with unit vectors I, J, K.

• In a diagonal form.

What is the purpose of finding the determinant in the matrix method for cross product?

• To check the perpendicularity of vectors.

• To find the magnitude of the vectors.

• To determine the unit vectors.

• To calculate the components of the resulting vector.

What is the result of the cross product of vectors A and B in the given example?

• 10 I + 61 J + 19 K

• -10 I + 61 J - 19 K

• -10 I - 61 J + 19 K

• 10 I - 61 J + 19 K

What does the right-hand rule help determine in the context of cross products?

• The magnitude of the cross product.

• The direction of the cross product vector.

• The angle between the vectors.

• The sum of the vectors.

How does the direction of A cross B compare to B cross A?

• A cross B is opposite to B cross A.

• They have the same direction.

• They are parallel.

• A cross B is perpendicular to B cross A.

What is the purpose of verifying the cross product using the dot product?

• To calculate the angle between vectors.

• To confirm the vectors are perpendicular.

• To find the magnitude of the cross product.

• To ensure the vectors are parallel.

What is the result of the dot product of vector C with vector A in the example?

• -133

• 0

• 183

• 50

Why is the dot product of vector C with vector A zero?

• Because they are parallel.

• Because they are in the same direction.

• Because they have the same magnitude.

• Because they are perpendicular.

What does a zero dot product indicate about two vectors?

• They have equal magnitudes.

• They are parallel.

• They are perpendicular.

• They are in opposite directions.