2.3.2 Vector Components

• Scalar quantities have both magnitude and direction.

  False
• What is the formula for calculating the vertical component of a vector?

  V_y = V \sin(\theta)</latex>
• The Cartesian coordinate system consists of two perpendicular axes: the x-axis and the y-axis
• What does \( \theta \) represent in the formulas for vector components?

  Angle with x-axis
• In the vector component formulas, \( V \) represents the magnitude
• What is the value of the y-component of a vector with magnitude 10 units and an angle of 30°?

  5 units
• The direction of the resultant vector is calculated using the formula \( \theta = \arctan(\frac{R_y}{R_x}) \).


  True
• What is the magnitude of the resultant vector when adding \( \mathbf{A} = (3, 4) \) and \( \mathbf{B} = (1, -2) \)?

  $\sqrt{20}$
• Velocity, force, and momentum are examples of vector quantities.

  True
• What formula is used to calculate the vertical component of a vector?

  $V_{y} =$$V \sin(\theta)$
• Where is the point (3, 2) located in the Cartesian coordinate system?

  3 units right, 2 units above
• How many units to the right of the origin is the point (3, 2) located?

  3
• What do the coordinates (x, y) represent in the Cartesian coordinate system?

  Distance from origin
• Calculate the x-component of a vector with a magnitude of 10 units and an angle of 30° with the x-axis.

  V_x \approx 8.66</latex>
• The direction of the resultant vector is calculated using the arctangent
• What function is used to calculate the direction of a vector from its components?

  Arctangent
• What is the direction of a vector with components \(V_x = 3\) and \(V_y = 4\)?

  $53.1^\circ$
• Vector components are projections of a vector onto the x and y axes of a coordinate
• The x-component of a vector with magnitude 10 and angle 30° is approximately 8.66.


  True
• What is the intersection point of the x and y axes in the Cartesian coordinate system called?

  Origin
• What formula is used to calculate the horizontal (x-component) of a vector?

  $V_{x} =$$V \cos(\theta)$
• The angle \( \theta \) in vector component formulas is measured with respect to the positive x-axis.


  True
• Steps to add or subtract vectors using their components

  1️⃣ Resolve each vector into its x and y components

  2️⃣ Add or subtract the corresponding components

  3️⃣ Reconstruct the resulting vector
• What is the x-component of the resultant vector when adding \( \mathbf{A} = (3, 4) \) and \( \mathbf{B} = (1, -2) \)?

  4
• What is the direction of the resultant vector when adding \( \mathbf{A} = (3, 4) \) and \( \mathbf{B} = (1, -2) \)?

  26.6°
• What are vector components?

  Projections on x and y axes
• The Cartesian coordinate system uses two perpendicular axes
• What is the origin in the Cartesian coordinate system?

  (0, 0)
• The Cartesian coordinate system uses two perpendicular axes to locate points on a two-dimensional plane.


  True
• What formula is used to calculate the horizontal (x) component of a vector?

  $V_{x} =$$V \cos(\theta)$
• Adding or subtracting vectors requires resolving them into their x and y components.


  True
• Steps to add or subtract vectors using their components

  1️⃣ Resolve each vector into its x and y components

  2️⃣ Add or subtract the corresponding components

  3️⃣ Reconstruct the resulting vector using its magnitude and direction
• The magnitude of a vector is its length
• What is a vector quantity defined by?

  Magnitude and direction
• What is the formula for calculating the horizontal component of a vector?

  $V_{x} =$$V \cos(\theta)$
• What are common examples of vector quantities?

  Velocity, force, momentum
• Match the component of the Cartesian coordinate system with its function:

  x-axis ↔️ Measures horizontal distance from the origin

  y-axis ↔️ Measures vertical distance from the origin

  Coordinates (x, y) ↔️ Uniquely identifies the location of a point
• What formula is used to calculate the vertical (y-component) of a vector?

  $V_{y} =$$V \sin(\theta)$
• What is the approximate value of the x-component of a vector with magnitude 10 units and an angle of 30°?

  8.66 units
• The magnitude of the resultant vector is calculated using the formula \( R = \sqrt{R_x^2 + R_y^2} \).


  True