Vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented graphically by an arrow.

Front

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

Back

To find the component form of a vector from point A(x1, y1) to point B(x2, y2), subtract the coordinates: .

Front

What is the formula for the dot product of two vectors u = and v = ?

Back

The dot product is calculated as u • v = ac + bd.

Front

What does it mean for two vectors to be orthogonal?

Back

Two vectors are orthogonal if their dot product is 0, indicating they are at a 90° angle to each other.

Front

How do you calculate the angle between two vectors?

Back

The angle θ between two vectors u and v can be found using the formula: cos(θ) = (u • v) / (|u| |v|), where |u| and |v| are the magnitudes of the vectors.

Front

What is the magnitude of a vector u = ?

Back

The magnitude of vector u is calculated as |u| = √(x² + y²).

Front

What is the resultant vector when two vectors are added?

Back

The resultant vector is the vector that represents the sum of two or more vectors, found by adding their corresponding components.

Front

If u = <3, 4> and v = <1, 2>, what is u + v?

Back

u + v = <3 + 1, 4 + 2> = <4, 6>.

Front

What is the 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

What is the unit vector in the direction of vector u = ?

Back

The unit vector in the direction of u is given by û = , where |u| is the magnitude of u.