A vector has magnitude and makes an angle of with the positive -axis. Given the information, which statement about the vector is true?
- It is a scalar because it has a magnitude.
- It is a vector because it has both magnitude and direction. (correct answer)
- It is a scalar because it has a direction.
- Its magnitude depends on where it is drawn on the plane.
Explanation: This question tests understanding of vectors as quantities that have both magnitude and direction. A vector quantity is characterized by having both a magnitude (size) and a direction, unlike scalar quantities which have only magnitude. The component form ⟨a, b⟩ means the vector has horizontal component a and vertical component b, which fully determines both its magnitude (√(a² + b²)) and direction (angle arctan(b/a) from positive x-axis). Choice B is correct because the vector is specified with both a magnitude of 20 and a direction of 30° from the positive x-axis. Choice A treats the vector as a scalar by omitting direction, but vectors require both magnitude and direction to be fully specified. To distinguish vectors from scalars, ask: does this quantity have a natural direction? Force, velocity, and displacement are vectors; mass, speed, and distance are scalars. Remember that two vectors are equal if they have the same magnitude and direction, even if they start at different points—position doesn't matter for vector equality.