2. VECTORS
Vectors are geometric representations of
magnitude and direction which are often
represented by straight arrows, starting at
one point on a coordinate axis and ending at
a different point. All vectors have a length,
called the magnitude.
7. HOW TO WRITE A VECTOR
PROPERLY
We use the cartesian plane to measure the
direction of vectors.
x-axis is always used to determine the
direction of the vectors
9. EXAMPLE:
A 60 S of W
A = vector
60 = the degrees
S and W = south and west
Starting from west, you go south 60
o
o
10. TO WRITE IT...
The vector first, followed by degrees and the
direction last.
14. VECTORS HAVE MAGNITUDES
To write a vector with magnitude, write the
direction with a absolute value sign:
lNlis N 40° S of W / lNl is 25km 40° S of W
N = if there is no magnitude/ value
16. TYPES OF VECTORS
2.Parallel Vectors = 2 vectors are parallel,
same direction different magnitude.
Example: 30km/20km
30KM
20KM
17. TYPES OF VECTORS
3.Anti - Parallel Vectors = 2 vectors are
parallel, same direction different magnitude.
Example: 30km/20km
30KM
20KM
18. TYPES OF VECTORS
4. Collinear Vectors = all of the three before
are collinear, because all vectors are at the
same line of action
19. TYPES OF VECTORS
4. Non- Collinear Vectors = 2 vectors that in
the same plane (cartesian) but not acting on
the same line of action. (not applicable at
180 and 0
20. ADDITION OF VECTORS
• Vectors have magnitude (length) and
direction.
• You add vectors graphically by placing
them tip-to-tail, not head-to-head.
• The resultant vector goes from the tail of
the first vector to the head of the last.
21. HEAD TO TAIL
• Draw to scale: pick a consistent scale (e.g.,
1 cm = 1km).
• Sequence matters: Position the tail of vector B
at the head of vector A, then vector C at B, etc.
• Connect the tail of the first to the head of the
last to form the resultan
22. HEAD TO TAIL
Example:
Point A = 1km east
Point B = 2km north
Point C = 3km east
Point D = ? (with the degrees)
Scale: 1cm (ruler) = 1km
23. SEATWORK
Example:
Point A = 4km east
Point B = 3km north
Point C = 2km east
Point D = ? (include degrees)
Scale: 1cm (ruler) = 1km
Editor's Notes
#3:scalars only have magnitude and quantity.
vectors = magnitude, direction and quantity.
#4:the arrow depends on what direction
teacher give example of direction of arrow
a capital letter with two bars/absolute value indicates its just magnitude.
vector also have head and tail
#6:northeast, southeast, northwest southwest if we don’t have direction, we wont know where we will go.
#7:its always measured with the horizontal axis
give example on how it must be measured using cartesian plane
#8:give each example of the 4 directions use the theta when writing an angle
#9:write it on the board canva sucks
1st step, draw a cartesian plane
2nd is put the x and y axis
3rd put the N, S, W, E
4th put the vector
5th graph a sample
put a theta from the angle
#10:do another example
45 degrees from east to north
continue the given earlier
#12:Quadrant 1 - 4 is 1 revolution
each quadrant has 90 degrees of angle, thus 360 for 1 revolution
q1 = 0 to 90
q2 = 90 - 180
q3 = 180 - 270
q4 = 270 - 360
#13:if we want to find the east of a degree we count at the bottom side of the protractor, if we want to find the degrees in the west we use the top set.
#15:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#16:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#17:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#18:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#19:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#20:90degrees<θ<180degrees = 180 is greater than your Reference angle/ your reference angle is less than 180 but greater than 90
#21:place the vector at the head/tip
pagsunodsunudin ninyo
#22:sample and answer is 3.5km 30 degrees north of east
or resultant D is 30 degrees 3.5km N of E
#23:sample and answer is 3.5km 30 degrees north of east
or resultant D is 30 degrees 3.5km N of E
