Unit 7 Review: Vectors

Front

What is a vector?

Back

A vector is a mathematical object that has both a magnitude (length) and a direction. It is often represented as an arrow in a coordinate system.

Front

How do you find the direction angle of a vector?

Back

The direction angle of a vector \( \langle x, y \rangle \) can be found using the formula: \( \theta = \tan^{-1}\left(\frac{y}{x}\right) \).

Front

What is the component form of a vector?

Back

The component form of a vector \( \vec{AB} \) from point A (x1, y1) to point B (x2, y2) is given by \( \langle x2 - x1, y2 - y1 \rangle \).

Front

How do you calculate the magnitude of a vector?

Back

The magnitude of a vector \( \langle x, y \rangle \) is calculated using the formula: \( ||\vec{v}|| = \sqrt{x^2 + y^2} \).

Front

What does it mean for two vectors to be parallel?

Back

Two vectors are parallel if they have the same or opposite direction, which means one is a scalar multiple of the other.

Front

What does it mean for two vectors to be orthogonal?

Back

Two vectors are orthogonal if their dot product is zero, indicating that they are at right angles to each other.

Front

How do you find the dot product of two vectors?

Back

The dot product of two vectors \( \vec{u} = \langle u_1, u_2 \rangle \) and \( \vec{v} = \langle v_1, v_2 \rangle \) is calculated as: \( \vec{u} \cdot \vec{v} = u_1v_1 + u_2v_2 \).

Front

What is the formula for vector addition?

Back

The sum of two vectors \( \vec{u} = \langle u_1, u_2 \rangle \) and \( \vec{v} = \langle v_1, v_2 \rangle \) is given by: \( \vec{u} + \vec{v} = \langle u_1 + v_1, u_2 + v_2 \rangle \).

Front

How do you subtract one vector from another?

Back

To subtract vector \( \vec{v} \) from vector \( \vec{u} \), use the formula: \( \vec{u} - \vec{v} = \langle u_1 - v_1, u_2 - v_2 \rangle \).

Front

What is a unit vector?

Back

A unit vector is a vector with a magnitude of 1. It is often used to indicate direction.