Vector Operations

Front

Define a vector.

Back

A vector is a mathematical object that has both a magnitude (length) and a direction. It is often represented as an ordered pair (x, y) in a two-dimensional space.

Front

What is vector addition?

Back

Vector addition is the process of adding two or more vectors together to get a resultant vector. This is done by adding their corresponding components.

Front

Calculate the sum of vectors v = <3, -5> and w = <-2, 3>.

Back

v + w = <3 + (-2), -5 + 3> = <1, -2>.

Front

What is scalar multiplication of a vector?

Back

Scalar multiplication involves multiplying a vector by a scalar (a real number), which scales the vector's magnitude without changing its direction.

Front

If u = <5, 2>, what is 3u?

Back

3u = 3 * <5, 2> = <15, 6>.

Front

Define the zero vector.

Back

The zero vector is a vector with a magnitude of zero and no specific direction, represented as <0, 0> in two-dimensional space.

Front

What is the formula for finding the resultant vector of two vectors?

Back

The resultant vector R of two vectors A and B is given by R = A + B, where R = .

Front

Calculate 2w + y if w = <2, -5> and y = <2, 0>.

Back

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

Front

What does it mean for two vectors to be equal?

Back

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

Front

If y = <2, 0> and z = <-1, -4>, find 3y - 2z.

Back

3y - 2z = 3 * <2, 0> - 2 * <-1, -4> = <6, 0> - <2, 8> = <4, -8>.