Vectors (NC Math 4)

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 two-dimensional space.

Front

How do you add two vectors?

Back

To add two vectors, you add their corresponding components. For example, if vector a = (x1, y1) and vector b = (x2, y2), then a + b = (x1 + x2, y1 + y2).

Front

What is the result of the vector operation 3y - 2z if y = <2, 0> and z = <-1, -4>?

Back

The result is <8, 8>.

Front

How do you subtract two vectors?

Back

To subtract two vectors, you subtract their corresponding components. For example, if vector a = (x1, y1) and vector b = (x2, y2), then a - b = (x1 - x2, y1 - y2).

Front

What is the result of the vector operation 3u - 2v if u = <5, 3> and v = <1, 5>?

Back

The result is <21, -6>.

Front

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

Back

The result is <6, -10>.

Front

What is the result of adding vectors a = (4, -5) and b = (-7, 4)?

Back

The result is (-3, -1).

Front

What is the result of subtracting vectors a = (4, -5) and b = (-7, 4)?

Back

The result is (11, -9).

Front

What does it mean for vectors to be equal?

Back

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

Front

What is the magnitude of a vector v = ?

Back

The magnitude of vector v is calculated as ||v|| = √(x² + y²).