Question

state parallelogram law of vectors derive an expression for the magnitude and direction of the reslutant vector​

Answer 1

Answer:

Showing results for state parallelogram law of vectors derive an expression for the magnitude and direction of the resultant vector​

Explanation:

Answer 2

Answer:

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 P and 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 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 △ OCD,

OC^2 =OD^2+CD^2

Now

CD=AC sinθ= Qsinθ

AD= ACcosθ= Qcosθ

OD= OA+ AD= P+ Qcosθ

Putting these values and representing resultant vector OC by vector R, magnitude of the resultant is given by

R^2=( P+Qcosθ)^2+(Qsinθ)^2=P^2+Q^2+2PQcosθ

In △ OCD,

tanα=CD/OD= Qsinθ/(P+Qcosθ)

Resultant acts in the direction making an angle α=tan^(−1)(Qsinθ/(P+Qcosθ)) with direction of vector P

Explanation:

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