Question

What is the equation for parallelogram law of vector addition

Answer 1

Answer:

Consider a parallelogram OABC as shown in the figure,

Parallelogram Law Of Vector Addition

Let P&Q be two adjacent sides of parallelogram, and R be the resultant vector obtained by addition of vectors P&Q,

Now, drop a perpendicular from C on OA so that they meet at A.

From right angled triangle ΔOCD,OC2=OD2+DC2

[OD=OA+AD]

R2=(OA+AD)2+DC2

R2=OA2+AD2+2OA.AD+DC2

From ΔADC, AC2=AD2+DC2

and also cosθ=ADAC

And hence R2=OA2+AC2+2OA.ACcosθ

And substituting A and B

R2=A2+B2+2A.Bcosθ

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Answer 2

Answer:

Explanation:

Refer the below attachment.