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What is Vector Product?

Vector product is a vector whose magnitude is equal to product of magnitude of two vectors and sine of smaller angle between them, the direction of it is perpendicular to the plane containing the two vectors and given by right handed screw rule.

vector product                                            vector product

Area of Triangle =

area of triangle

Area of Parallelogram =

area of Parallelogram
 

What is Scalar Product?

Scalar product is the product of magnitude of two vectors and cosine of angle θ  between them

P × Q = PQ cosƟ

Scalar Product

If P = Pxî + Pyĵ + Pzk̂ and Q = Qxî + Qyĵ + Qz

Then P ×Q = PxQz + PyQy + PzQz …….. dot product

scalar product

From the above equation we know that Power is a Scalar Quantity as it is a scalar product of two Vector Quantities.

What is Lami’s theorem?

When three forces are acting at a point and they are in equilibrium, then each force is directly of proportional to the sine of the angle between the other two forces.

Lami’s theorem

Let us consider A, B and C be three forces acting at a point O. as these three forces are in equilibrium, the point is at rest. Let α, β and γ be the angles opposite to the forces A, B and C respectively.

So, as per Lami’s theorem

lami's theorem

What is the formula for Torque acting due to couple (or) Moment of couple ?

Two equal and opposite parallel forces acting at different points in a body constitute a couple. Pedals of bicycles is the example for couple, where the two forces are equal but acting in opposite direction.

Torque acting due to couple (or) Moment of couple Torque is calculated by the product of either of forces forming the couple and the arm of the couple.

Torque = one of the force × perpendicular distance between the forces.

formula for Torque acting due to couple (or) Moment of couple

In the figure, two equal forces F and F acting on the arm LM. Let us consider O as the mid-point of the arm .The forces F and F, which constitute a couple, are acting in opposite direction.

From the figure, the formula or equation for Principle of moments is given as,

Moment of couple or torque = F × LM.

The moment becomes zero when the forces acting on the body have the same line of action. When the forces are at right angles to the arm (θ=900), the torque is maximum.

What is the formula or equation for Principle of moments?

As per the principle of moments,“The sum of the clockwise moments about any point must be equal to the sum of anti-clockwise moments about the same point, provided that the body is in equilibrium under the action of a number of parallel forces.”

According to the principle of moments,

Sum of anti-clockwise moments = sum of clockwise moments

The formula or equation for Principle of moments is given as,

                                m1d1 + m2d2 =m3d3 + m4d4

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