Vectors

Front

What are equivalent vectors?

Back

Vectors that have the same magnitude and direction, such as u and -u.

Front

How do you find the component form of a vector given two points?

Back

Subtract the coordinates of the initial point from the terminal point. For example, for points R(-12, 4) and S(28, -17), the vector RS is given by S - R = (28 - (-12), -17 - 4) = (40, -21).

Front

If u = <3, 7>, what is 2u?

Back

2u = <2*3, 2*7> = <6, 14>.

Front

How do you perform vector subtraction?

Back

To subtract vector u from vector v, subtract the corresponding components: v - u = .

Front

Given u = <3, 7> and v = <-5, 4>, what is 2v - 3u?

Back

2v - 3u = <2*-5, 2*4> - <3*3, 3*7> = <-10, 8> - <9, 21> = <-19, -13>.

Front

What is the component form of the vector AB if A(2, 4) and B(-8, 7)?

Back

AB = B - A = <-8 - 2, 7 - 4> = <-10, 3>.

Front

Define a vector in mathematics.

Back

A vector is a quantity that has both magnitude and direction, represented as an ordered pair or triplet of numbers.

Front

What is the zero vector?

Back

The zero vector is a vector with a magnitude of zero and no specific direction, represented as <0, 0>.

Front

How do you find the magnitude of a vector?

Back

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

Front

What is the dot product of two vectors?

Back

The dot product of vectors u = and v = is u · v = u1*v1 + u2*v2.