The document introduces the concept of vectors in a plane, explaining their definition as pairs of direction and magnitude, represented by arrows. It covers the magnitude and direction of vectors, components, types of vectors including equivalent, collinear, opposite, and null vectors, and provides assessment tests on these topics. Additionally, it includes problems on finding the magnitude and direction of specific vector pairs along with an answer key.

1. INTRODUCTION OF
VECTOR IN A PLANE

2. What are Vectors?
 Vectors are pairs of a direction and a magnitude. We
usually represent a vector with an arrow:
 The direction of the arrow is the direction of the
vector, the length is the magnitude.
 Vector is denoted = where the point A is called the tail
or the initial point and point B is the terminal point or
the head.

3. Magnitude of a Vector
The magnitude of a vector is the distance between the initial
point P and the end point Q. in symbols the magnitude of is written as .
if the coordinates of the initial point and the end point of a
vector is given, the Distance Formula can be used to find its magnitude.
Q(
P(

4. Direction of a vector
The direction of a vector is the measure of the
angle it makes with a horizontal line.
One of the following formulas can be used to
find the direction of a vector:
where x is the horizontal change and y is the
vertical change or where ( is the initial point and
( is the terminal point.

5. COMPONENTS
Vector components are the change in x and the change in y.
In situations in which vectors are directed at angles to the customary
coordinate axes, a useful mathematical trick will be employed to transform the
vector into two parts with each part being directed along the coordinate axes.
=
+
Northwest vectors have a northward and westward part.
=
+
An upward and rightward vector has an upward and rightward part.

6. TYPES OF VECTORS
Equal vector –Vector of the same
length and direction are called
equivalent.
Collinear vector –Two vectors are
collinear, if they lie on the same line
or parallel lines.

7. Opposite vector – if they have the
same magnitude but opposite
direction.
Null vector – is the dimensional vector
of length (i.e., the vector with
components, each of which is 0). A
second meaning of null vector when
applied to a matrix is a nonzero vector
with the property that Ax = 0

8. ASSESSMENT
TEST I: Write True or False ( 1 point each)
1. Vectors are used to represent velocity, force and tension
2. A component form of a vector is the ordered pair that
describe the changes in the x and y values.
3. The Associative Law, which state the order or addition
does not depend on which pair of vector is added first: (a
+ b) + c = a + (b + c)
4. If then is stated by the associative property of addition
of vectors.
5. A null vector is a vector with a zero magnitude.

9. Test II: Solving: Find the magnitude and direction of the
ordered pair (2 points each)
1. A(2,3) and B(4,6)
2. C(1,1) and D(5,3)
3. P(6,7) and Q(5,2)
Draw or Illustrate:
4. Given that . Find the sum of the vectors.
5. If A = and c = 2 Find Ca.

10. Answer Key
I. True or False
1.T
2.T
3.F
4.F
5.T

11. II. Solving
1. A(2,3) and B(4,6) 2. C(1,1) and
B(5,3)
or
or 2

12. 3. P(6,7) and Q(5,2)

13. 4. Given that Find the sum of the vectors.
Solution:
Q
R
P
5
4
2
3
1
1
0
2 3 4 5
y
x

14. 5. If A = and c = 2, Find cA.
cA = 2
cA =
cA =