Vectors

Front

What is a vector?

Back

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

Front

What are the components of a vector?

Back

The components of a vector are its projections along the axes of a coordinate system, typically represented as (x, y) in 2D.

Front

How do you find the magnitude of a vector \( \mathbf{v} = \langle a, b \rangle \)?

Back

Front

What is the direction angle of a vector?

Back

Front

How do you add two vectors \( \mathbf{u} \) and \( \mathbf{v} \)?

Back

To add vectors, sum their corresponding components: \( \mathbf{u} + \mathbf{v} = \langle u_x + v_x, u_y + v_y \rangle \).

Front

What is the formula for the dot product of two vectors \( \mathbf{u} \) and \( \mathbf{v} \)?

Back

Front

What is the cross product of two vectors?

Back

Front

What is the significance of the angle between two vectors?

Back

The angle between two vectors affects their dot product and can indicate whether they are orthogonal, parallel, or neither.

Front

How do you find the vertical and horizontal components of a vector \( \mathbf{v} = \langle a, b \rangle \)?

Back

The vertical component is \( b \) and the horizontal component is \( a \).

Front

What is the unit vector in the direction of a vector \( \mathbf{v} \)?

Back