2.8 Vectors I

• Vectors and scalars
• Representing vectors: column vectors and notation
• Addition and subtraction of vectors
• Multiplication of a vector by a scalar
• Magnitude of a vector
• Translation as a vector

• distinguish between vectors and scalars
• represent vectors in column form
• add and subtract vectors
• multiply a vector by a scalar
• calculate the magnitude of a vector

“Why is knowing how far not enough without knowing which way?”

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1. Vectors and column form
   40 min · 2 practice tasks · quiz
   Quantities that need a direction, and how to write them down.
2. Adding, subtracting and scaling vectors
   40 min · 2 practice tasks · quiz
   Combining vectors by components and by drawing, and what a scalar multiple does.
3. Writing and drawing vectors
   40 min · 1 practice tasks · quiz
   Name a directed line segment in the accepted ways, then draw it to scale on a grid.
4. Equivalent vectors
   40 min · 1 practice tasks · quiz
   Two vectors are equal when they have the same magnitude and the same direction, wherever they are drawn.
5. The negative of a vector
   40 min · 1 practice tasks · quiz
   Reversing a vector changes every sign, gives the zero sum, and names the reverse journey.
6. Triangle and parallelogram laws
   40 min · 1 practice tasks · quiz
   Add two vectors by completing a triangle or a parallelogram; both give the same resultant.
7. The resultant of several vectors
   40 min · 1 practice tasks · quiz
   Chain three or more vectors head to tail; the closer from start to finish is the resultant.
8. Column vectors on the Cartesian plane
   40 min · 1 practice tasks · quiz
   Read a column from two plotted points, and plot the image of a point after a given column.
9. Position vectors
   40 min · 1 practice tasks · quiz
   The position vector of a point is the vector from the origin to that point, and it shares the point's coordinates.
10. The vector from A to B
    40 min · 1 practice tasks · quiz
    AB equals the position vector of B minus the position vector of A.
11. Magnitude in different situations
    40 min · 1 practice tasks · quiz
    Find the length of a vector, of a sum or difference, and the distance between two points.
12. The midpoint of a line segment
    40 min · 1 practice tasks · quiz
    The position vector of the midpoint of AB is half the sum of the position vectors of A and B.
13. Translation as a transformation
    40 min · 1 practice tasks · quiz
    A translation maps every point by the same vector; the image is congruent and faces the same way.
14. Combining translations
    40 min · 1 practice tasks · quiz
    Two translations one after another are equivalent to the single translation given by the sum of their vectors.
15. Vectors in real life
    40 min · 1 practice tasks · quiz
    Use column vectors for map displacements, sports passes and combined movements in Kenyan settings.