Addition of Vectors

The Right Triangle |Component of vectors |Resultant vectors by component method

28 July 2012

REDG 2011

1

The Right Triangle (c) (a)

(b) c = a +b
2 2 2 2 2

Solve for a and b.

a2 = c2 -b2 b2 = c2 -a2

c = a +b
28 July 2012

REDG 2011

2

The Right Triangle

hypotenuse opposite

 adjacent 28 July 2012 REDG 2011 3

The Right Triangle

adjacent



hypotenuse

opposite
28 July 2012 REDG 2011 4

The Right Triangle

The opposite always faces opposite to the reference angel 

28 July 2012

REDG 2011

5

The Right Triangle
Identify the opposite, adjacent, and hypotenuse in each right triangle below.

 z y 1 x  a
28 July 2012

a  2 b b 4 c
REDG 2011

y c x p  5 s q
6

3



z

Trigonometric Functions opposite sinθ= hypotenuse adjacent cosθ= hypotenuse opposite tanθ= adjacent

28 July 2012

REDG 2011

7

The Right Triangle
Write the equations to get the values of the unknown side (represented by letters in red color).

 z y 1 x  a
28 July 2012

a  2 b b 4 c
REDG 2011

y c x p  5 s q
8

3



z

Resultant Vectors

28 July 2012

REDG 2011

9

Resultant Vectors
Hint: Identify the adjacent and opposite

How do we determine for the x-component? What about for the y-component?
28 July 2012 REDG 2011 10

Resultant Vectors
Hint: The resultant vector is the hypotenuse of the triangle.

From the given x-component and y-component, how do you get the resultant vector?
28 July 2012 REDG 2011 11

Resultant Vectors

From the given x-component and y-component, how do you determine the angle?
28 July 2012 REDG 2011 12

Resultant Vectors d R = x 2 +y 2 = 300 2 +200 2 = 130000 =360m

Given the following vectors, determine the magnitude of the resultant.
28 July 2012 REDG 2011 13

Resultant Vectors
y  =tan   x -1  200  =tan  300   
-1

=33.7O

Given the following vectors, determine the direction of the resultant vector.