Vectors

• What is the topic of the video?

  Vectors
• What do column vectors describe?

  A journey from a start point to an end point
• How can we represent a vector in algebra?

  By naming it with a letter, like A
• How are vectors indicated in exam papers?

  Using bold letters
• What do underlined letters represent in handwritten math?

  Vectors
• How do we denote the vector from point O to point X?

  With an arrow above OX
• What is the vector from O to X named?

  A
• What is the vector from O to Y called?

  B
• What happens when you reverse the direction of a vector?

  You change the sign of all terms
• How is the vector from Y to O represented?

  As negative B
• How is the vector from X to O represented?

  As negative A
• How can we describe the vector from X to Y using A and B?

  As negative A plus B
• What is the vector from X to Y equal to?

  A plus B
• How can you express the vector from Q to P?

  As -5A plus B
• What does the vector from P to R equal?

  4A plus 2B
• How do you find the vector from P to S?

  By adding PR and RS
• How do you express the vector from O to M?

  As 2A plus 3B
• What is the vector from A to M?

  3B
• What is the vector from O to N equal to?

  3B plus A
• How do you find the vector from N to B?

  By adding -3B minus A to 6B
• What is the vector from N to B simplified to?

  3B minus A
• How do you express the vector from A to X?

  As 3/4 of A
• What is the vector from X to B equal to?

  1/4 of A
• How do you express the vector from B to Y?

  As 2/7 of BC
• What is the total length of the line from O to C?

  5B
• How do you find the vector from A to C?

  By adding 2A and 6B
• Why is it often easier to write answers as fractions in vector questions?

  Fractions simplify calculations in vector problems
• How can we express the journey from X to Y using vectors?

  As the sum of vectors XB and BY
• What fraction of the vector from A to B is the vector from X to B?

  One-fourth
• How do we express the vector from B to Y in terms of the vector from B to C?

  As two-sevenths of the vector BC
• What is the vector from X to B if the vector from A to B is $-3A +$$B$?


  $-3/4A +$$1/4B$
• What is the vector from B to C if it is given as $4B$?


  $2/7 \cdot 4B$
• How do we combine the vectors from X to B and B to Y?

  By adding their respective components
• What is the common denominator used to simplify the fractions for vector B?

  28
• What is the simplified form of the combined vector from X to Y?

  $3/4A +$$39/28B$
• What is the relationship between parallel vectors?

  One vector is a multiple of the other
• How can we express the vector from C to D if it is parallel to the vector from A to B?

  As a multiple of the vector AB
• What must be true for three points A, B, and C to be collinear?

  The vectors AB and BC must be parallel
• How do we show that points P, Q, and R are collinear?

  By finding two vectors with a common point
• What is the vector from P to Q if it is calculated as $-6A +$$9B$?


  $-6A +$$9B$