Question

state the parallelogram's law of vector addition and derive an resultant of two vector p and q inclined to each other at angle alpha​

Answer 1

Answer:

Statement of Parallelogram Law

If two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.

Explanation:

Let P and Q be two vectors acting simultaneously at a point and represented both in magnitude and direction by two adjacent sides OA and OD of a parallelogram OABD as shown in figure.

Let θ be the angle between P and Q and R be the resultant vector. Then, according to parallelogram law of vector addition, diagonal OB represents the resultant of P and Q.

So, we have

R = P + Q

Now, expand A to C and draw BC perpendicular to OC.

From triangle OCB,

OB²= OC²+BC²

or, OB²= (OA +AC)²+BC² .......{ i }

In triangle ABC,

cos0 =BC/AB

or, BC = AC sin0

or, BC = OD sin0 = Q sin0 [since, OB=OD=Q]