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EXAMPLE 12 : A rope from a car is tied to the peak of a frame A, exerts a force of 400 N along the rope. A 500kg weight is suspended from the other end of the rope. What is the total force acting on the frame-A by the rope?
Solution:
The force exerted by weight 500 Kg. is due to the gravity
= mg
= (500 ) ( 9.81)
= 4905 N
Let it be 'b' \ | b | = 4905 N.
Let the force exerted by the car be 'a' and | a | = 400 N.
Draw the parallelogram of forces as F1, F2 & F.
Let 'c' be the resultant force. Then using law of cosine we get
EXAMPLE 13 : The magnitudes of vectors P,Q and R ( shown in figure) are | P | = 10 units ,
| | Q | = 8 units and | R | = 20 units. Find the magnitude and direction of their sum A.
Solution:
The given vectors are resolved along  as shown in the figure 27.
We will tabulize the calculation as -
The magnitude of the resultant A will be
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