The document explains the resolution of vectors into their components along the x and y axes. It covers concepts such as unit vectors, their representation, and how to derive components of a given vector based on angles. Additionally, it differentiates between resolution and composition of vectors and includes practical examples and exercises for resolving vectors.

3. Lets revise

5. RESOLUTION OF VECTOR SPLITTING OF GIVEN VECTOR INTO ITS COMPONANTS
Y
X
∝
O
A
X component of a is acos∝
Y component of a is asin∝
acos∝
asin∝
Given vector OA is split into two components along x axis and y axis
NOTE: In case of coplanar vector system ,given vector is resolved (split) into two
Components one along x axis and other along y axis .such components are called
Rectangular or Orthogonal vectors
B
C

6. Resolution VS Composition
Resolution म्हणजे दिलेल्या व्हेक्टरची विभागणी करणे आणण Composition म्हणजे
दिलेल्या िोन व्हेक्टरची बेरीज करणे ,म्हणजेच Resultant काढणे .
ह्याचा अर्थ Resolution आणण Composition ह्या विरुध्ि Process आहेत
θ
Given single vector
Splitting into components
Given two vectors
Combining given vectors
Resolution Composition

7. ELEPHANT STONE LIFTING TWO PERSONS
RESULTANT
EFFECT PRODUCED TWO VECTORS,FORCES
COMPONANTS
X
Y
R

8. Lets practice resolution
Resolve following vectors in two components
45
10N
45
10 cos 45
10 sin 45
30
100N
For Practice
10 N
१० N ची िेक्टर line ज्याश्याशी अँगल करते ,ती बाजू cos च्या
स्िरूपात येते आणण उरलेली िुसरी बाजू sin च्या स्िरूपात येते

9. UNIT VECTOR
What is magnitude of Unit vector
It is unit ,single length
What is use of this concept
Unit vector only use to indicate Direction
1)A unit vector is a vector that has a
magnitude of 1 unit. A unit vector is also
known as a direction vector.
2)Representation :It is represented using a lowercase letter with a cap (‘^’) symbol along with
it.. such as b^( read b hat or cap)
3)any vector can become a unit vector by
dividing it by the vector’s magnitude.
4) Unit Vector= vector/magnitude of vector

10. I , j , k Directions Z
X
Y
i
k
j
X
Y
i
j
O
O
TWO AXES SYSTEM
Rectangular components
THREE AXES SYSTEM
Space components
The unit vector along x, y and z axes are
represented as i, j and k respectively.
ONE AXIS SYSTEM
O i X

12. Lets explore unit vector I want to move 10 km towards North,
remember 10 gives us magnitude and North gives direction
If A= 2i what is meaning ? Meaning is vector is directed
along x axis and whose magnitude is two times
magnitude of unit vector ie 2 ,as unit vector has
unit magnitude.
If B= 3 i what is meaning ? Meaning is vector is directed
along Y axis and whose magnitude is three times
magnitude of unit vector ie 3, as unit vector has
unit magnitude.

13. CONCEPT OF UNIT VECTOR
Vector= magnitude × direction
Direction given by Unit Vector
scalar

14. RECTANGULAR COMPONANTS OF VECTOR IN THREE DIMENSIONS

15. O
A
X
Y
Z
E
B
D
C
a
plane

19. FINAL WORDS ABOUT UNIT VECTOR

20. WORKSHEET 5
1
2
3
4 A force of 10 N is inclined at an angle of 30° with horizontal ,find out its
Components along horizontal and vertical directions
5 Find out angle made by A = I +2j + k vector with X,Y and Z Axes respectively