Understanding Vectors in 3D Space

What is the main difference between a point and a vector in 3D space?

• A point has direction, a vector does not.

• A vector is location-specific, a point is not.

• A vector has magnitude, a point does not.

• A point can be moved without changing its identity, a vector cannot.

How is a vector represented differently from a point?

• Vectors use parentheses, points use angled brackets.

• Vectors use curly brackets, points use square brackets.

• Vectors use square brackets, points use curly brackets.

• Vectors use angled brackets, points use parentheses.

What happens to a vector if its direction is reversed?

• It becomes a different vector.

• Its magnitude doubles.

• It remains the same vector.

• Its magnitude becomes zero.

How do you find a vector between two points?

• Divide the coordinates of the terminal point by the initial point.

• Subtract the initial point's coordinates from the terminal point's coordinates.

• Multiply the coordinates of the two points.

• Add the coordinates of the two points.

What is the vector PQ if P is (5, 1, -3) and Q is (-1, 4, 6)?

• (-6, 3, 9)

• (6, -3, -9)

• (4, -5, -3)

• (-4, 5, 3)

What term is used to describe the length of a vector?

• Direction

• Velocity

• Magnitude

• Amplitude

How is the magnitude of a vector calculated?

• By subtracting the components and taking the square root.

• By multiplying the components and taking the square root.

• By squaring each component, adding them, and taking the square root.

• By adding the components and taking the square root.

What is the magnitude of the vector (3, 2, 6)?

• 7

• 11

• 9

• 5

If a vector has components (1/2, 5/2, -7/2), what is its magnitude?

• 3√5/2

• √50/4

• √75/4

• 5√3/2

What is a vector with a magnitude of 1 called?

• Zero vector

• Null vector

• Unit vector

• Scalar vector