This document is the first chapter of a mathematics textbook on vectors. It introduces vectors as quantities that have both magnitude and direction, and can be represented by directed line segments. The chapter covers representing and notating vectors, performing vector addition and subtraction, and defining and calculating the dot and cross products of vectors. It also introduces unit vectors in multiple dimensions and the right hand rule for cross products.

1. SM10203 Mathematics ii
Chapter 1 : Vector i
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3. Scalars and Vectors
Scalar is a number which expresses quantity.
Examples: mass, volume, energy, money
Vector is a quantity which has both magnitude
and direction. The magnitude of a vector is a
scalar.
Examples: displacement, velocity, acceleration,
electric field
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4. Vector are represented by
directed line segment.
Length of the line segment
is the magnitude of the
vector.
Direction of the line
segment is the direction of
the vector.
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6. Same vector - Line segment with
the same length and direction.
In each case the vector start a
specific point then moves 2 units
to the left and 5 units up.
Notation :
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7. Position vector -
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13. The general notation for a n-dimensional vector is
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14. The i-unit vector points in
the positive x-direction.
The j-unit vector points in
the positive y-direction.
The k-unit vector points in
the positive z-direction
(upward).
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15. Vector Arithmetic
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17. Vector subtraction : Subtract “b” from “a”.
Graphically,Method 1: add the negative of “b” to “a”.
Draw a vector from the start of “a” to the end of “b”. This is
the resultant vector.
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18. Method 2
Start vector “b” at the start of vector “a”.
Then draw the resultant vector from the end of “b”
to the end of “a”.
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28. Dot Product
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29. Dot Product
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31. Dot Product
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32. Dot Product
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43. Cross Product
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44. Cross Product
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45. Cross Product
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46. Cross Product
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47. Cross Product
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48. Cross Product
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49. Right Hand Rule
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50. Cross Product
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51. Cross Product
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52. Cross Product
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53. Cross Product
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