Vector Addition and Properties

What two fundamental properties define a vector?

• Magnitude and mass

• Direction and speed

• Magnitude and direction

• Length and time

How is the magnitude of a vector typically represented in a graphical illustration?

• By the angle of the arrow

• By the length of the arrow

• By the thickness of the arrow

• By the color of the arrow

What defines two vectors as "equivalent vectors"?

• They have the same starting point.

• They have the same magnitude but different directions.

• They have the same magnitude and direction.

• They represent different physical quantities.

When adding two vectors, u and v, using the head-to-tail method, how is the vector sum (u + v) represented?

• A vector from the tail of v to the head of u.

• A vector from the tail of u to the head of v.

• A vector that bisects the angle between u and v.

• A vector perpendicular to both u and v.

In the parallelogram method for vector addition, if two vectors u and v start at the same point, their sum (u + v) is represented by:

• One of the sides of the parallelogram.

• The shorter diagonal of the parallelogram.

• The diagonal of the parallelogram starting from the common origin of u and v.

• A vector perpendicular to the parallelogram.

What happens to a vector when it is multiplied by a positive scalar greater than 1?

• Its direction is reversed.

• Its magnitude decreases.

• Its magnitude increases, and its direction remains the same.

• Both its magnitude and direction change.

If a vector 'u' is multiplied by a negative scalar, such as -1, what is the resulting effect on the vector?

• The vector's magnitude increases.

• The vector's direction is flipped 180 degrees.

• The vector becomes a scalar.

• The vector's magnitude becomes zero.

How are vectors represented using components in a 2D coordinate system, distinguishing them from ordered pairs?

• Using parentheses (a1, a2)

• Using curly braces {a1, a2}

• Using angle brackets

• Using square brackets [a1, a2]

Which of the following properties of addition apply to vectors?

• Commutative and Distributive

• Associative and Identity

• Commutative and Associative

• Distributive and Inverse

In a 3D coordinate system, what are the standard basis vectors (unit vectors) along the x, y, and z axes, respectively?

• i, j, k

• x, y, z

• u, v, w

• a, b, c