Question

1.What is the First Condition of Equilibrium?

2.Explain what Pythagorean Theorem is and give the formula. ?

3.The Scalar Product or otherwise known Dot Product of two vectors is the sum of the products of their respective components. What does the scalar product give us? And when is the product zero?

Answer 1

1. The first condition of Equilibrium is that the net force on the system has to be zero regardless at which point it is being acted upon, which means that sum of all the forces acting on the system has to be zero.

Fnet = 0

=>

2.  The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and c,

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

This formula is mostly used in vectors where a,b represent the components of the vector and c represents the magnitude of the vector.

3. The dot product tells you what amount of one vector goes in the direction of another. For instance, if you pulled a box 10 meters at an inclined angle, there is a horizontal component and a vertical component to your force vector. So the dot product in this case would give you the amount of force going in the direction of the displacement, or in the direction that the box moved. This is important because work is defined to be force multiplied by displacement, but the force here is defined to be the force in the direction of the displacement.

Now the dot product is given as v1.v2 = v1v2cos , where is the angle between the vectors v1 and v2. Now for this to be zero either v1 or v2 or both has to be zero or the angle has to be 90 which means that the vectors have to perpendicular to each other.