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What is the answer if vector A is multiplied with vector B?

In vector multiplication, there are two types of multiplication: One in which the result is a scalar and the other in which the result is a vector.

Accordingly the two types of products of vectors are:

Scalar product (also called dot product) denoted byA.B

Vector product (also called cross product) denoted by AxB

A.B  = AB cos Θ, where Θ is the angle between the directions of A and B

The physical meaning of dot product is that, “The product of the magnitude of one vector and the magnitude of the component of the other vector in the direction of the first vector.”

AxB = AB sinΘ \hat{n}

The direction of cross product is given by right hand cork screw rule

cross product

Difference between Scalar Product and Vector Product

“What is the difference between dot product and cross product?” [The question was posted by Salman)

Define area vector in simpler terms

Area VectorArea vector is a vector whose magnitude is equal to the area and is directed normal to the surface.

Area as such is a scalar. So, Area vector is defined as above for use in calculations and defining some other terms like torque on a current carrying loop in a magnetic field etc.

Examples of scalar product and vector product

Kashan asks:

“will you give me min 10 examples 0f scalar product and vector product known at xii level”

I am just strating the list; members please contribute more as comments

Scalar Product

  1. work F.s
  2. Power F.v
  3. Potential energy of a dipole P.E

 

Vector Product

  1. Torque on a dipole = PxE
  2. Lorentz magnetic force F=qvxB
  3. Torque =rxF

 

 

Difference between dot product and cross product

Shashi Kant asked:

“What is difference between cross product and dot product?”

 

Answer:

If the product of two vectors is a scalar quantity it is called scalar product or dot product.

If the product of two vectors is a vector quantity it is called vector product or cross product.

Vector resolution and addition

Zeenath Asks:

Sir please send me the answers with the reasons and steps

  1. the drawing on the left shows two vectors A and B, and the drawing on the right shows their components.

    The scalar components of these vectors are:

    When the vectors A and B are added, the resultant vector is R, so that RAB. What are the x– and y-components of R?
  2. the displacement vectors A and B, when added together, give the resultant vector R, so that RAB. Use the data in the drawing to find the magnitude R of the resultant vector and the angle q that it makes with the +x axis.

 

 

Answer

In the first question as you can see that the X components (Ax and Bx being equal and opposite will cancel each other and therefore the X com ponent of the resultant is zero.

The Y components will add up and therefore the Y component of resultant = 3.4+3.4 = 6.8 m and this itself is the magnitude of the resultant as the X components have canceled out.

Hnit for Answer to the second question

Short circuiting, overloading, Area vector

Gopika asked:

What is the basic difference between short circuiting & overloading?
Why is area considered as both scalar and vector quantity?

 

Ans:

Short circuiting

As such the words suggest, the circuit becomes shorter. If there is a failure in insulation or some other means by which the two wires (phase and neutral) comes into electrical contact, the circuit gets shortened as the current always chooses the path which has got least resistance. Since the resistance of the shorted circuit is less a heavy current flows.

Overloading

In house hold circuiting we are using parallel combination of the different appliances. Every instrument is connected in parallel to the supply. Whenever a new apparatus is switched on, it draws more current. If the current drawn by all the devices connected in a circuit is more than the maximum current rating for the given circuit, the condition is called overloading.

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