A scalar quantity describes magnitude (size) only (Mnemonic: s in scalar stands for "size")
A vector quantity describes both magnitude and direction
(Mnemonic: v in vector looks like the end of an arrow)
1
What are some examples of scalar quantities?
2
What are some examples of vector quantities?
3
Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector.
By convention, the length of a vector
arrow is proportional to the magnitude of the vector.
2 m
4 m
4
Two vectors are the same when they have the same size and direction
A
D
B
C
E
F
5
Vector Addition
2 + 2 ≠ 4 (at least not always)
Depending on the directions of the two vectors, the answer to this question could be any number from 0 to 4. 6
When adding vectors your final answer must include BOTH magnitude and direction of the resultant (final) vector.
7
Adding Parallel Vectors
Case 1: Vectors point in the SAME direction
A + B = C
Magnitude of C
A
A
+
B
B
Direction of C
8
Case 2: Vectors point in OPPOSITE directions
A + B = C
A
B
+
Magnitude of C
BA
B
A
Direction of C
9
Adding NON­Parallel Vectors
Geometric Methods
A
B
+
10
Method 1: Triangle Method
nd
1. Move the 2 vector so it starts at the end of the first vector.
2. The Resultant vector will start at the start of st
the 1 vector & end at nd
the end of the 2 vector
A
A
B
+
B
11
Method 2: Parallelogram Method
1. Move the vectors so they start at the same point.
A
+
B
2. The Resultant vector A
will be the diagonal of the parallelogram B
formed by the two vectors. It will start at the same point as the vectors themselves.
12
Use one of the two geometric methods of vector addition to show that A+ B =B +A
13
Vector Components
Any vector can be split into x and y components
A
θ
14
15
16
17
Use geometric method of vector additiont o show that Ax + Ay = A
Ay
A
θ
Ax
18
Do Now: For each vector pair, find the resultant:
(a)
(b)
(c)
(d)
(e)
(f)
19
Which pair(s) of vectors can produce a resultant of 7.7? Note: only magnitudes are listed
(a) 10 and 6
(b) 5.5 and 2.1
(c) 11 and 2
(d) 7.7 and 7.7
20
Which pair of vectors will produce the vector sample problem 1
(1) largest resultant
(2) smallest resultant
(a) (b)
(c)
(d)
21
Which pair of vectors will produce a resultant shown below?
(a)
(b)
(c)
(d)
22