Question

State the parallelogram law of vector addition and derive the expression for its magnitude
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Answer 1

Answer:

its used in vectors

Explanation:

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Answer 2

Parallelogram law states that if two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.

In the figure, $\large\rm { \vec{P} \ and \ \vec{Q}}$ are two vectors.with magnitudes equal to length OA and OB respectively and making angle θ between them. Complete the parallelogram, OACB,

Join diagonal OC , that makes angle α with vector $\large\rm { \vec{P}}$

According to parallelogram law of vectors the resultant is represented by the diagonal passing through the point of contact of two vectors.

To find the magnitude of resultant , produce a perpendicular CD to meet OA produced to D.

From $\large\rm { \triangle}$ OCD,

$\large\rm { OC^{2} = OD^{2} + CD^{2}}$

Now, $\large\rm { \vec{C} D = \vec {A} C \ \sin \theta = \vec {Q} \ \sin \theta}$

$\large\rm { AD = \vec {A} C \ \cos \ \theta = \vec {Q} \ \cos \theta}$

Putting these values and representing resultant vector OC by $\large\rm { \vec{R}}$ , magnitude of the resultant is given by

In $\large\rm { \triangle}$ OCD,

$\large\rm { \tan \ \alpha = \frac { \vec{Q} \ \sin \theta}{ \vec {P} + \vec {Q} \ \cos \theta}}$