Vectors - Day 2

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented as an ordered pair (x, y) in a coordinate system.

Front

How do you find the magnitude of a vector v = ?

Back

The magnitude of a vector v = is calculated using the formula |v| = √(x² + y²).

Front

Given vectors u = and v = , how do you find 2u - 3v?

Back

To find 2u - 3v, multiply each component of u by 2 and each component of v by 3, then subtract the corresponding components: 2u - 3v = <2a - 3c, 2b - 3d>.

Front

What is the component form of a vector from point A(x1, y1) to point B(x2, y2)?

Back

The component form of the vector AB is given by .

Front

How do you calculate the resultant vector of two vectors u and v?

Back

The resultant vector of u and v is found by adding their corresponding components: R = .

Front

What is the significance of the initial and terminal points of a vector?

Back

The initial point is where the vector starts, and the terminal point is where it ends. The vector's direction and magnitude are determined by these points.

Front

If w = <2, -5> and y = <2, 0>, what is 2w + y?

Back

2w + y = <2*2 + 2, 2*(-5) + 0> = <4 + 2, -10 + 0> = <6, -10>.

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d between two points is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the magnitude of the vector ?

Back

The magnitude is calculated as || = √(a² + b²).

Front

What does it mean for two vectors to be equal?

Back

Two vectors are equal if they have the same magnitude and direction, which means their corresponding components are equal.