4.3 Vectors

• A vector represents both magnitude and direction
• A column vector represents vectors as vertical lists of components
• To subtract vector b from vector a, reverse the direction of b and add it to a.

  True
• To subtract vector b from vector a, you must first reverse the direction of vector b to get -b
• Vector subtraction involves reversing the direction of the subtrahend and then adding it to the minuend.


  True
• In vector addition, the vectors are placed head-to-tail
• Match the vector operation with its graphical representation:

  Vector Addition ↔️ Placing vectors head-to-tail

  Vector Subtraction ↔️ Reversing subtrahend direction
• When a vector is multiplied by a negative scalar, its direction is reversed.


  True
• What is the effect on a vector when multiplied by zero?

  Null vector
• The direction of a vector is typically expressed in degrees or radians
• The direction of a vector is expressed in degrees or radians.


  True
• What two properties does a vector represent?

  Magnitude and direction
• An arrow over a letter in vector notation indicates a vector.

  True
• The graphical representation of a vector using arrow notation shows its direction and magnitude
• What graphical method is used to represent vector addition?

  Head-to-tail
• What are combined in vector addition to obtain a resultant vector?

  Magnitudes and directions
• Scalar multiplication changes the direction of a vector if the scalar is negative.


  True
• What happens to the magnitude of a vector when multiplied by a scalar?

  Changes proportionally
• What is the formula to calculate the magnitude of a vector in column vector notation?

  \sqrt{x^{2} + y^{2}}
• Bold letters and arrows over letters are used to differentiate vectors from scalars.


  True
• Steps for adding two vectors head-to-tail

  1️⃣ Place vectors a and b head-to-tail

  2️⃣ Draw the resultant vector from the tail of a to the head of b
• What is the first step to finding the vector that, when added to vector b, would give vector a?


  Reverse the direction of **b**
• Steps for graphical representation of vector addition

  1️⃣ Combine magnitudes and directions of two vectors

  2️⃣ Place vectors head-to-tail
• What is combined in vector addition to obtain the resultant vector c?


  Magnitudes and directions
• In vector subtraction, what is added to vector a after reversing the direction of vector b?


  -b
• What does scalar multiplication of a vector change if the scalar is positive?

  Magnitude
• In scalar multiplication, the magnitude of a vector changes proportionally to the scalar
• What happens to the direction of a vector when multiplied by a negative scalar?

  Reversed
• The magnitude of a vector is always a positive value.


  True
• What is the formula to calculate the magnitude of a column vector [x, y] in two dimensions?

  \sqrt{x^2 + y^2}</latex>
• Match the vector notation with its feature:

  Column Vector ↔️ Components [x, y]

  Bold Letters ↔️ Denotes vectors

  Coordinate Form ↔️ Shows displacement from origin
• A column vector represents a vector as a vertical list of its components
• In arrow notation, what does the length of the arrow represent?

  Magnitude
• Graphical representation of vectors complements their symbolic notations.


  True
• Vector subtraction involves reversing the direction of the subtrahend and then adding it to the minuend.


  True
• To subtract vector b from a, reverse the direction of b to get -b and then add it to a.
• Multiplying a vector by the scalar zero results in a null vector.
• The magnitude of a vector is always a positive value.

  True
• Match the vector notation with its features:

  Column Vector ↔️ Components [x, y]

  Bold Letters ↔️ a, b

  Coordinate Form ↔️ (x, y)
• The direction of a vector is the angle it makes with the x-axis.