The parallelogram law states that when two concurrent forces F1 &F2 acting on a body are represented by two adjacent sides of a parallelogram the diagonal passing through their point of concurrency represents the resultant force R in magnitude and direction
No, the diagonals of a parallelogram are not normally congruent unless the parallelogram is a rectangle.
False
Either diagonal of a parallelogram divides the parallelogram into two triangles of equal areas. Thus area of triangle abd = half that of the parallelogram abcd. The required ratio is 1 / 2.
Yes the diagonals of a parallelogram have the same midpoint since they bisect each other.
I can't offer a full proof, but I can suggest some possibilities that will lead you to your proof. In a parallelogram, you can easily demonstrate that the angles formed by a cord extending between parallel lines and the parallel lines themselves, and that are formed on opposite sides of the cord, are equal. This will work for both pairs of triangles in the parallelogram, and can be applied to all of the angles at the corners of the parallelogram. This will lead you to demonstrating that the pairs of triangles "pointing" to each other (not adjacent pairs) are similar, and in fact congruent. From there it is not difficult to establish that the connected sections of the two interior cords are equal.
it is applicable to two forces only
The parallelogram law of forces says that the sum of two forces is equivalent to the parallelogram formed by placing the first vector as starting from the origin and the second starting from the head of the first. This can be proven through trigonometric derivation of triangle angles and sides.
it is applicable to two forces only
How it is related is given in the following link: http://blog.oureducation.in/to-verify-the-law-of-parallelogram-of-forces/
The parallelogram law of forces can be applied to any situation where multiple forces are acting on an object. The launching of a stunt person from a cannon in a circus is a prime example. To achieve a certain angle of launch with a certain velocity, an initial velocity must be applied to the person, but countering that is the force of gravity. So, the initial velocity is one leg of the parallelogram and the other leg is the force of gravity.
it states "if two force, which act simultaneously on a particle be represented in ma
In a parallelogram of forces, the resultant force is represented by the diagonal of the parallelogram drawn from the initial point of the forces to the opposite corner. The magnitude and direction of the resultant force are determined by the length and orientation of this diagonal in the parallelogram.
Concurrent coplanar forces have their lines of action intersecting at a common point, allowing them to be resolved using the parallelogram law of forces. Non-concurrent coplanar forces have their lines of action not intersecting at a common point, requiring the use of the triangle law of forces for resolution.
The resultant of two vectors can be computed analytically from a vector parallelogram by determining the diagonal of the parallelogram. The diagonal represents the resultant vector, which can be found by adding the two vectors tip-to-tail. This method is based on the parallelogram law of vector addition.
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"If two vector quantities are represented by two adjacent sides or a parallelogram then the diagonal of parallelogram will be equal to the resultant of these two vectors."
The parallelogram law of vectors states that if two vectors are represented by the sides of a parallelogram, then the diagonal of the parallelogram passing through the point of intersection of the two vectors represents the resultant vector. This means that the sum of the two vectors is equivalent to the diagonal vector.