Vectors & Ellipses

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 find the angle between two vectors?

Back

The angle θ between two vectors a and b can be found using the formula: cos(θ) = (a • b) / (|a| |b|), where • denotes the dot product.

Front

What is the dot product of two vectors?

Back

The dot product of two vectors a = and b = is calculated as a • b = a1*b1 + a2*b2.

Front

What is the magnitude of a vector?

Back

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

Front

What is a unit vector?

Back

A unit vector is a vector with a magnitude of 1, indicating direction only. It is found by dividing the vector by its magnitude.

Front

How do you convert a vector to component form?

Back

To convert a vector to component form, express it as an ordered pair (x, y) where x and y represent the horizontal and vertical components, respectively.

Front

What is the component form of the vector <8, 2>?

Back

The component form of the vector <8, 2> is simply <8, 2>, indicating 8 units in the x-direction and 2 units in the y-direction.

Front

What is the significance of the angle between vectors?

Back

The angle between vectors indicates the direction relationship between them; an angle of 0° means they point in the same direction, while 90° means they are perpendicular.

Front

How do you find the unit vector in the same direction as a given vector?

Back

To find the unit vector in the same direction as vector v, divide v by its magnitude: u = v / |v|.

Front

What is the component form of the vector <7, 3>?

Back

The component form of the vector <7, 3> is <7, 3>, indicating 7 units in the x-direction and 3 units in the y-direction.