Q1: According to Law of Triangle of Forces

ANS:E - if the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order.

This statement refers to the principle known as the Law of Parallelogram of Forces. According to the Law of Parallelogram of Forces, if two forces acting on a particle are represented in magnitude and direction by the adjacent sides of a parallelogram, then the resultant of these forces is represented in magnitude and direction by the diagonal of the parallelogram that passes through the point of intersection of the two sides. However, the statement provided seems to refer to a similar concept applied to triangles rather than parallelograms. Let's break down the statement to understand it better: "if the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order." This statement essentially means that if two forces acting on a particle are represented by two adjacent sides of a triangle (taken in order), then their resultant force (the force that represents their combined effect) will be represented by the third side of the triangle, taken in opposite order. To visualize this concept, consider a triangle where two sides represent the two forces acting on a particle. If you close the triangle by connecting the endpoints of these two sides, the resultant force—the force that would be required to replace the effects of the two original forces—will be represented by the third side of the triangle, taken in the opposite order. This principle illustrates how vector addition works in mechanics. It's a fundamental concept used to determine the net force acting on an object when multiple forces are applied simultaneously. The Law of Parallelogram of Forces is a special case of this principle when forces are represented using a parallelogram instead of a triangle.