Vector Operations

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

Back

The result is <8, 8>.

Front

What is the formula for subtracting two vectors?

Back

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

Front

Given v = <3, -5> and w = <-2, 3>, what is v + w?

Back

The result is <1, -2>.

Front

How do you find the components of a vector given an equation?

Back

To find the components of a vector v such that v + = , rearrange to v = .

Front

If u = <5, 2> and v = <1, -1>, what is u + v?

Back

The result is <6, 1>.

Front

What is the result of the vector operation a - b if a = <-2, 0> and b = <-4, -8>?

Back

The result is <2, 8>.

Front

Define the term 'magnitude' in the context of vectors.

Back

Magnitude refers to the length or size of a vector, calculated using the formula √(x² + y²) for a vector .

Front

What is the geometric interpretation of vector addition?

Back

Vector addition can be visualized as placing the tail of the second vector at the head of the first vector, forming a resultant vector.