Question 1

What is the difference between a scalar and a vector?

Accepted Answer

A scalar has magnitude only (e.g. speed, mass, temperature). A vector has both magnitude and direction (e.g. velocity, force, displacement).

Question 2

How do you add two vectors?

Accepted Answer

Add corresponding components: (a, b) + (c, d) = (a+c, b+d). Geometrically, place vectors tip to tail and draw the resultant from start to finish.

Question 3

What is the magnitude of vector (a, b, c)?

Accepted Answer

|v| = √(a² + b² + c²). For 2D vector (a, b): |v| = √(a² + b²).

Question 4

What is a unit vector?

Accepted Answer

A vector with magnitude 1. Found by dividing a vector by its magnitude: v̂ = v/|v|. The unit vectors i, j, k point along the x, y, z axes.

Question 5

What is a position vector?

Accepted Answer

A vector from the origin O to a point P, written as OP or p. The position vector of a point (3, 4) is 3i + 4j.

Question 6

How do you find the vector AB?

Accepted Answer

AB = b − a (position vector of B minus position vector of A). This gives the vector from A to B.

Question 7

What is the dot product (scalar product) of two vectors?

Accepted Answer

a·b = |a||b|cosθ, where θ is the angle between them. In component form: (a₁, a₂, a₃)·(b₁, b₂, b₃) = a₁b₁ + a₂b₂ + a₃b₃.

Question 8

How do you use the dot product to find the angle between two vectors?

Accepted Answer

cosθ = (a·b)/(|a||b|). Find the dot product, divide by the product of magnitudes, then take cos⁻¹.

Question 9

What does it mean if the dot product of two vectors is zero?

Accepted Answer

The vectors are perpendicular (θ = 90°, so cos90° = 0). E.g. i·j = 0.

Question 10

What are parallel vectors?

Accepted Answer

Two vectors are parallel if one is a scalar multiple of the other: b = λa for some scalar λ. Parallel vectors have the same or opposite directions.

Vectors Flashcards

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