Vector Flashcard #1

Front

Given an initial point A (2, 4) and terminal point B (-8, 7), find the component form of the vector AB.

Back

The component form of vector AB is 〈-10, 3〉.

Front

What is the angle between two vectors if the result is 142.13°?

Back

The angle between the vectors is 142.13°.

Front

Find the magnitude of the vector 〈10, -8〉.

Back

The magnitude of the vector 〈10, -8〉 is 12.81.

Front

Given v = 〈3, -5〉 and w = 〈-2, 3〉, what is 2v + 3w?

Back

2v + 3w = 〈0, -1〉.

Front

Determine the direction and magnitude of the vector 〈7, 18〉.

Back

Direction 68.7°, Magnitude 19.3.

Front

What is the formula to find the magnitude of a vector 〈x, y〉?

Back

The magnitude is given by √(x² + y²).

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: B - A.

Front

What is the formula to find the angle between two vectors?

Back

The angle θ can be found using cos(θ) = (u • v) / (|u| |v|).

Front

What does the dot product of two vectors represent?

Back

The dot product represents the product of the magnitudes of the vectors and the cosine of the angle between them.

Front

What is the component form of a vector from point (1, 2) to point (4, 6)?

Back

The component form is 〈3, 4〉.