Vector Practice

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented as an ordered pair (x, y) in a coordinate system.

Front

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

Back

The magnitude of a vector \( \mathbf{v} \) is calculated using the formula: \( ||\mathbf{v}|| = \sqrt{a^2 + b^2} \).

Front

What is the component form of a vector?

Back

The component form of a vector \( \mathbf{v} \) is expressed as \( \langle a, b \rangle \), where 'a' is the horizontal component and 'b' is the vertical component.

Front

If \( A(1, -3) \) and \( B(-5, 1) \) are points, what is the component form of vector \( \overrightarrow{AB} \)?

Back

The component form of vector \( \overrightarrow{AB} \) is \( \langle -6, 4 \rangle \).

Front

What does the horizontal component of a vector represent?

Back

The horizontal component of a vector represents the change in the x-direction.

Front

What does the vertical component of a vector represent?

Back

The vertical component of a vector represents the change in the y-direction.

Front

How do you determine if a vector has a specific magnitude?

Back

To determine if a vector has a specific magnitude, calculate its magnitude using the formula and compare it to the given value.

Front

What is the magnitude of the vector \( \langle 9, -3 \rangle \)?

Back

The magnitude of the vector \( \langle 9, -3 \rangle \) is \( 3\sqrt{10} \).

Front

What is the significance of the direction of a vector?

Back

The direction of a vector indicates where the vector points in space, which is crucial for understanding its application in physics and engineering.

Front

How can you represent a vector graphically?

Back

A vector can be represented graphically as an arrow pointing from the initial point to the terminal point, with the length of the arrow indicating the magnitude.