4.3 Vectors

• Vectors are commonly used to represent physical quantities like velocity and force.


  True
• Vectors can be represented using column notation.


  True
• Steps to add two vectors using their components:

  1️⃣ Add the horizontal components

  2️⃣ Add the vertical components

  3️⃣ Write the result in column notation
• What is the formula for adding two vectors in terms of their components?

  \[x1 + x2, y1 + y2]
• Scalar multiplication is different from vector addition and subtraction because it scales the vector's magnitude
• What is the result of multiplying the vector `[3]` by the scalar 2?

  \[6, 0]
• Match the vector component with its description:

  Horizontal ↔️ Left-right direction

  Vertical ↔️ Up-down direction
• In column notation, the top number represents the horizontal component of the vector.
• What is the result of multiplying the vector [3] by the scalar 2?

  [6]
• Vectors are often used to represent physical quantities like displacement, velocity, and force.
• Steps to add or subtract vectors using column notation:

  1️⃣ Perform operation on horizontal components

  2️⃣ Perform operation on vertical components

  3️⃣ Combine results into a new vector
• What is the process of multiplying a vector by a scalar called?

  Scalar multiplication
• Match the vector component with its description:

  Horizontal ↔️ Left-right direction

  Vertical ↔️ Up-down direction
• The magnitude of a vector is always a positive value.


  True
• Parallel vectors must have the same direction, while collinear vectors can have any direction as long as they lie on the same line.


  True
• Steps to solve vector equations

  1️⃣ Set horizontal components equal

  2️⃣ Set vertical components equal

  3️⃣ Solve the resulting equations
• Adding vectors involves adding their horizontal and vertical components separately.


  True
• Vector addition and subtraction operate on the individual vector components
• Match the vector component with its description:

  Horizontal ↔️ Left-right direction

  Vertical ↔️ Up-down direction
• To subtract two vectors, you subtract their corresponding horizontal and vertical components.


  True
• To subtract two vectors, you subtract their corresponding components
• Scalar multiplication scales the magnitude of a vector but does not change its direction.


  True
• In column notation, the top number represents the horizontal component, and the bottom number represents the vertical component.


  True
• Vector addition is performed by adding corresponding components.


  True
• A vector has both magnitude and direction.

  True
• Match the vector component with its description:

  Horizontal ↔️ Left-right movement

  Vertical ↔️ Up-down movement
• Scalar multiplication changes the magnitude of a vector but not its direction.

  True
• What is the magnitude of the vector `[3]`?

  5
• What is the defining characteristic of parallel vectors?

  Same direction
• What is an example of two parallel vectors given in the study material?

  [3] and [6]
• A vector is a quantity with both magnitude and direction
• Solving the vector equation [2y - 3] = [1] results in y = 2.


  True
• To subtract two vectors, you subtract their corresponding horizontal and vertical components
• Scalar multiplication scales the magnitude of a vector while keeping its direction the same

  True
• Scalar multiplication scales the magnitude
• Scalar multiplication scales the magnitude
• What function is used to find the direction of a vector?

  Inverse tangent
• The direction of the vector [3] is 0°
• Adding two position vectors involves adding their corresponding components
• Parallel vectors have the same direction, even if they have different magnitudes.