Vectors Day 2- Angles of vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction.

Front

How do you find the magnitude of a vector?

Back

The magnitude of a vector \( \langle a, b \rangle \) is calculated using the formula \( \sqrt{a^2 + b^2} \).

Front

What is the direction of a vector?

Back

The direction of a vector is the angle it makes with the positive x-axis, measured counterclockwise.

Front

How do you determine the angle of a vector \( \langle x, y \rangle \)?

Back

The angle \( \theta \) can be found using \( \theta = \tan^{-1}(\frac{y}{x}) \).

Front

What is the horizontal component of a vector \( \langle x, y \rangle \)?

Back

The horizontal component is the x-value of the vector, which is \( x \).

Front

What is the vertical component of a vector \( \langle x, y \rangle \)?

Back

The vertical component is the y-value of the vector, which is \( y \).

Front

How do you find a vector with a specific magnitude in the same direction as another vector?

Back

To find a vector with magnitude \( m \) in the same direction as \( \langle a, b \rangle \), use the formula \( \langle \frac{a}{\sqrt{a^2 + b^2}} \cdot m, \frac{b}{\sqrt{a^2 + b^2}} \cdot m \rangle \).

Front

What is the magnitude of the vector \( \langle 0, -9 \rangle \)?

Back

The magnitude is 9.

Front

What is the magnitude of the vector \( \langle -5, 12 \rangle \)?

Back

The magnitude is 13.

Front

What is the direction of the vector \( \langle -11, 5 \rangle \)?

Back

The direction is 155.6°.