Topic Content:
- Parallelogram Law of Vectors
- Derivation of the Law
- Direction of the Resultant Vector
This is used when two vectors are inclined at an angle to each other and it states that:
If two forces acting at a point are represented in magnitude and direction by the sides of the parallelogram drawn from that point, their resultant is represented in magnitude and direction by the diagonal of the parallelogram drawn from that point.
Derivation of the Law:
Let θ be the angle between B and D and R be the resultant vector. Then, according to parallelogram law of vector addition, diagonal OE represents the resultant of B and D.
So, we have
R = B + D
Now, expand O to F and draw EF perpendicular to OF.
From ΔOFE,
OE2 = OF2 + EF2
But OF = OD + DF
∴ OE2 = (OD + DF)2 + EF2 ……..(i)
In ΔDEF,
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How did we get 2DB cosO
(D + Bcosθ)^2
(D + Bcosθ)(D + Bcosθ)
open the brackets
D^2 + DBcosθ + DBcosθ + B^2cos^2θ
D^2 + 2DBcosθ + B^2cos^2θ
Splendid