Vector Algebra and Components Flashcards (10 cards)

What defines a scalar quantity?

A single value with magnitude but no direction.

What properties define a vector quantity?

It has magnitude, direction, and sense.

How are two-dimensional vectors represented using Cartesian coordinates?

As an ordered pair, $A=(x,y)$.

What determines a vector’s quadrant in the Cartesian coordinate system?

The signs of its x- and y-coordinates.

What is the vector sum of the x- and y-components?

$A=A_x+A_y$

What are the component formulas for a vector at angle $\theta$ from the positive x-axis?

$A_y=A\sin\theta$ and $A_x=A\cos\theta$.

What formula gives the magnitude of a vector with perpendicular components $A_x$ and $A_y$?

$A=\sqrt{A_x^2+A_y^2}$

What magnitude and direction characterize a unit vector?

It has magnitude 1 and the same direction as the vector it represents.

Which unit vectors point along the x-, y-, and z-axes, respectively?

$\vec{i}$, $\vec{j}$, and $\vec{k}$.

How can a vector’s direction angle be determined from its components?

Use inverse trigonometric functions on the component ratios.