Vector Components

Front

What are vector components?

Back

Vector components are the projections of a vector along the axes of a coordinate system, typically represented as x (horizontal) and y (vertical) components.

Tags

NGSS.HS-PS2-4

Front

How do you calculate the x component of a vector?

Back

The x component can be calculated using the formula: x = magnitude * cos(θ), where θ is the angle of the vector with respect to the x-axis.

Front

How do you calculate the y component of a vector?

Back

The y component can be calculated using the formula: y = magnitude * sin(θ), where θ is the angle of the vector with respect to the y-axis.

Front

What is the relationship between the magnitude of a vector and its components?

Back

The magnitude of a vector can be found using the Pythagorean theorem: magnitude = √(x² + y²).

Front

What is the significance of the angle in vector components?

Back

The angle determines the direction of the vector and affects the values of its x and y components.

Front

If a vector has a magnitude of 100 N and makes an angle of 30° with the x-axis, what is its x component?

Back

x = 100 * cos(30°) = 86.6 N.

Front

If a vector has a magnitude of 100 N and makes an angle of 30° with the x-axis, what is its y component?

Back

y = 100 * sin(30°) = 50 N.

Front

What is the formula to find the resultant vector from its components?

Back

The resultant vector R can be found using R = √(x² + y²) and the angle θ = tan⁻¹(y/x).

Front

What is the unit of measurement for vector components?

Back

Vector components are measured in units relevant to the context, such as Newtons (N) for force or meters (m) for displacement.

Front

How do you represent a vector graphically?

Back

A vector is represented graphically by an arrow, where the length indicates the magnitude and the direction indicates the direction of the vector.