Introduction to 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 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 • denotes the dot product.

Front

What is the magnitude of a vector?

Back

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

Front

What is the dot product of two vectors?

Back

The dot product of two vectors u and v is calculated as u • v = |u| |v| cos(θ), where θ is the angle between them.

Front

What does it mean for vectors to be orthogonal?

Back

Vectors are orthogonal if their dot product is zero, meaning they are at a right angle (90 degrees) to each other.

Front

How do you represent a vector in component form?

Back

A vector can be represented in component form as v = , where x and y are the horizontal and vertical components, respectively.

Front

What is the resultant vector?

Back

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

Front

What is the significance of the direction of a vector?

Back

The direction of a vector indicates where it points in space, which is crucial for understanding its effect in physical applications.

Front

How do you subtract one vector from another?

Back

To subtract vector v from vector u, you can add the negative of v to u: u - v = u + (-v).

Front

What is a unit vector?

Back

A unit vector is a vector with a magnitude of 1, used to indicate direction without regard to magnitude.