Understanding Vectors and Their Properties

What is the difference between scalar and vector quantities?

• Scalars have both magnitude and direction, while vectors have only magnitude.

• The difference is that scalars have only magnitude, while vectors have both magnitude and direction.

• Vectors are always larger than scalars in value.

• Scalars can be represented as arrows, while vectors cannot.

Which of the following is a vector quantity: speed, velocity, or temperature?

• mass

• velocity

• distance

• acceleration

How do you find the components of a vector given its magnitude and direction?

• x = r * cos(θ), y = r * sin(θ)

• x = r + θ, y = r - θ

• x = r * sin(θ), y = r * cos(θ)

• x = r * tan(θ), y = r * sec(θ)

What is a unit vector and how is it represented mathematically?

• A unit vector is a vector with a magnitude of 1, represented mathematically as \( \hat{v} = \frac{\mathbf{v}}{||\mathbf{v}||} \).

• A unit vector is represented as $ \mathbf{v} = ||\mathbf{v}|| $.

• A unit vector can have any magnitude greater than 1.

• A unit vector is a vector with a magnitude of 0.

If a vector has a magnitude of 5 units and points in the positive x-direction, what are its components?

• (0, 0, 5)

• (5, 0, 0)

• (0, 5, 0)

• (5, 5, 0)

How can you graphically represent a vector in a coordinate system?

• Use a dotted line to connect the origin to the vector's endpoint.

• Plot the vector's components as separate points without connecting them.

• Draw a circle around the origin to represent the vector.

• Draw a directed line from the origin to the point defined by the vector's components in a coordinate system.

What is the formula to calculate the magnitude of a vector given its components?

• magnitude = sqrt(x^2 + y^2 + z^2)

• magnitude = x^2 + y^2 - z^2

• magnitude = x + y + z

• magnitude = |x| + |y| + |z|

How do you convert a vector into a unit vector?

• Divide each component of the vector by its magnitude.

• Add a constant value to each component.

• Take the square root of each component.

• Multiply each component by its magnitude.

What does the direction of a vector indicate in a graphical representation?

• The orientation or pointing direction of the vector.

• The length of the vector.

• The magnitude of the vector.

• The color of the vector.

Why is it important to distinguish between scalar and vector quantities in physics?

• Scalars are used only in mathematical equations, not in physics.

• It is important to distinguish between scalar and vector quantities because scalars have only magnitude while vectors have both magnitude and direction, affecting problem-solving in physics.

• Vector quantities are always larger than scalar quantities.

• Scalars can have direction while vectors cannot.