Vectors

What is the result of multiplying a vector by a vector?

• A number (scalar product)

• Another vector

• A matrix

• A tensor

Define a vector.

• A quantity that has both magnitude and direction.

• A quantity that has only magnitude.

• A point in space with no direction.

• A line segment with a fixed length.

How do you represent a vector in component form?

• As an ordered pair (x, y) or (x, y, z) in three dimensions.

• As a single number in one dimension.

• As a list of all possible values of the vector.

• As a graphical representation on a coordinate plane.

What is the result of subtracting one vector from another?

• A scalar value.

• A matrix.

• A vector.

• A point in space.

What is the dot product of two vectors?

• A scalar value obtained by multiplying corresponding components and summing the results.

• A vector obtained by adding the two vectors together.

• A measure of the angle between two vectors.

• A scalar value obtained by dividing the magnitudes of the two vectors.

What makes two vectors equivalent?

• They have the same direction and magnitude.

• They have different directions but the same magnitude.

• They are perpendicular to each other.

• They have the same direction but different magnitudes.

What is the difference between a vector and a scalar?

• A vector has only magnitude, while a scalar has both magnitude and direction.

• A vector has both magnitude and direction, while a scalar has only magnitude.

• A vector is a type of scalar that includes direction.

• Vectors and scalars are the same; they both represent quantities.

What is the unit vector in the direction of a vector v?

• A vector with a magnitude of 1 in the same direction as v.

• A vector with a magnitude greater than 1 in the same direction as v.

• A vector that is perpendicular to v.

• A vector with a magnitude of 0 in the same direction as v.

What is the cross product of two vectors?

• A scalar quantity that represents the magnitude of the vectors.

• A vector that is perpendicular to the plane formed by the two vectors.

• The sum of the two vectors in the same direction.

• A vector that lies in the same plane as the two vectors.

What is the zero vector?

• A vector with a magnitude of zero and no direction.

• A vector with a magnitude of one and a direction.

• A vector that points in the positive x-direction.

• A vector with a magnitude of zero and a direction towards the origin.