Calculus III: The Cross Product (Level 4 of 9)

Which of the following operations is defined only for vectors in three-dimensional space?

• Dot product

• Cross product

• Scalar multiplication

• Vector addition

What is the result of a cross product between two vectors?

• A complex number

• A matrix

• A vector

• A scalar

What is the result of a cross product between two scalars?

• A scalar

• A matrix

• A vector

• Undefined

When verifying orthogonality, what should the dot product of the cross product with the original vectors equal?

• 1

• 0

• Infinity

• The magnitude of the vectors

How can you obtain a second unit vector orthogonal to two given vectors?

• By subtracting the vectors

• By adding the vectors

• By dividing the unit vector by its magnitude

• By multiplying the unit vector by -1

What is the first step in finding a vector orthogonal to a plane defined by three points?

• Calculate two vectors on the plane

• Add the coordinates of the points

• Find the midpoint of the points

• Normalize the vectors

What is the significance of a vector orthogonal to a plane?

• It is perpendicular to the plane

• It is parallel to the plane

• It is a tangent to the plane

• It lies on the plane