Vectors — Flashcards & Quiz

Q1: What is the difference between a scalar and a vector quantity?

A scalar has magnitude only (e.g. speed, distance, mass, energy, time). A vector has both magnitude and direction (e.g. velocity, displacement, acceleration, force). Vectors are represented by arrows whose length indicates magnitude and orientation indicates direction.

Q2: How do you add two vectors that are not in the same direction?

Use the head-to-tail method: draw the first vector, place the tail of the second at the head of the first. The resultant is from the tail of the first to the head of the last. For perpendicular vectors, use Pythagoras. For others, use the sine and cosine rules or resolve into components.

Q3: How do you resolve a vector into perpendicular components?

For a vector V at angle θ to the horizontal: horizontal component V_x = Vcosθ; vertical component V_y = Vsinθ. This allows 2D problems to be solved as two independent 1D problems.

Q1: Speed is a vector quantity because it describes how fast an object is moving.

Answer: FALSE

Speed is a SCALAR — it has magnitude only (how fast). Velocity is the vector equivalent, having both magnitude and direction. Speed = |velocity|.

Q2: Two vectors of magnitude 3 N and 4 N always produce a resultant of 7 N.

Answer: FALSE

The resultant depends on the angle between them. Maximum = 3 + 4 = 7 N (same direction). Minimum = 4 - 3 = 1 N (opposite direction). At 90°: √(9+16) = 5 N. The resultant ranges from 1 N to 7 N.

Q3: When resolving a vector into components, the component is always smaller than the original vector.

Answer: TRUE

Each component = V×cosθ or V×sinθ, and since cos and sin are ≤ 1 (for 0° < θ < 90°), each component is smaller than the original vector. The original vector is the hypotenuse of the right triangle formed by its components.