HPC 6.1 Intro 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 write a vector in component form?

Back

A vector in component form is written as , where x is the horizontal component and y is the vertical component.

Front

What is the formula to find the magnitude of a vector ?

Back

The magnitude of a vector is calculated using the formula: √(x² + y²).

Front

What does the direction of a vector represent?

Back

The direction of a vector indicates the angle at which the vector is pointing, usually measured from the positive x-axis.

Front

How do you add two vectors u and v?

Back

To add two vectors u and v, you add their corresponding components: u + v = .

Front

What is the horizontal component of a vector given its magnitude and angle?

Back

The horizontal component can be found using the formula: magnitude * cos(angle).

Front

What is the vertical component of a vector given its magnitude and angle?

Back

The vertical component can be found using the formula: magnitude * sin(angle).

Front

If a vector has a magnitude of 10 and an angle of 30°, what are its components?

Back

Horizontal component: 10 * cos(30°) = 8.66; Vertical component: 10 * sin(30°) = 5.

Front

What is the resultant vector?

Back

The resultant vector is the vector that results from adding two or more vectors together.

Front

How do you find the angle of a resultant vector?

Back

The angle of a resultant vector can be found using the formula: tan(angle) = vertical component / horizontal component.