Vectors and Scalars

Flashcards about vectors, scalars, and vector operations based on lecture notes.

What are vectors?

Quantities that have both magnitude and direction.

What are scalars?

Quantities that have only magnitude.

Give examples of vectors.

Displacement, velocity, acceleration, and force.

Unless specified otherwise, how is the angle 𝜃 measured?

Counterclockwise direction from the positive x-axis.

What is vector decomposition?

Expressing a vector in terms of its x- and y-components rather than magnitude and direction.

What are the two methods for vector addition?

Graphical and algebraic (component) methods.

What is the graphical method for vector addition also known as?

Tip-to-tail rule (parallelogram rule)

What are the steps for the component method of vector addition?

Find all components, Add up all x-components, and add up all y-components, Find magnitude and direction of the resultant vector.

What notation is used for unit vectors in 3D?

𝚤̂, 𝚥̂ and 𝑘

What are the two ways to take products of vectors?

Scalar product (dot product) and vector product (cross product).

How is the scalar product calculated?

a dot b = a_yb_y + a_xb_x

How is the angle 𝜃 between two vectors calculated using the scalar product?

theta = arcos[(a dot b)/ab]

What does the vector cross product return?

A vector, c, which is perpendicular to both 𝑎⃗ and 𝑏⃗, and whose magnitude is the area of the parallelogram spanned by 𝑎⃗ and 𝑏⃗.

What is the anticommutative property of cross products?

𝑎⃗ × 𝑏⃗ = −𝑏⃗ × 𝑎⃗

What is the magnitude of the cross product of two vectors a and b equal to?

𝑐 = 𝑎𝑏 sin 𝜃