Vector Operations and Applications

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 add two vectors?

Back

To add two vectors, you add their corresponding components. For example, if u = and v = , then u + v = .

Front

What is the formula for finding the magnitude of a vector?

Back

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

Front

How do you find the resultant of two vectors?

Back

The resultant of two vectors can be found by adding them using vector addition, which involves adding their components.

Front

What does it mean to scale a vector?

Back

Scaling a vector means multiplying it by a scalar (a real number), which changes its magnitude but not its direction.

Front

Given u = <3, 7> and v = <-5, 4>, find 2u - 3v.

Back

2u - 3v = <21, 2>.

Front

If a turtle moves from coordinate P = (3,2) to Q = (5,6), what vector models the turtle's motion?

Back

The vector modeling the turtle's motion is <2, 4>.

Front

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).

Back

The magnitude of vector AB is 10.

Front

If w = <2, -5> and y = <2, 0>, find 2w + y.

Back

2w + y = <6, -10>.

Front

What is the direction of a resultant force of 7 N north and 5 N west?

Back

The direction is 54.962 degrees north of west.