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# distinguish between scalar product and vector product of two vectors

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## Difference between scalar product dot product and vector product

Difference between scalar product dot product and vector product

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Difference between scalar product dot product and vector product

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Difference between scalar product ( dot product) and vector product.

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Dot product or scalar product Cross product or vector product

If the product of two vectors is a scalar quantity, the product is called scalar product or dot product. If the product of two vectors is a vector quantity then the product is called vector product or cross product.

The dot product is defined by the relation:

A . B = AB Cos θ The cross product is defined by the relation:

A × B = AB Sinθ u

The scalar product obeys commutative law as

A.B =B.A The vector or cross product does not obey commutative law

A×B ≠B×A

If two vectors are perpendicular to each other then their scalar product is zero.

A.B =0 If two vectors are parallel to each other, their vector product is zero.

A×B=0 Suggest Corrections 76

SIMILAR QUESTIONS

Q. What is the difference between the dot product and cross product of two vectors?Q.

Assertion: Statement I: The dot product of one vector with another vector may be a scalar or a vector.

Reason: Statement-II: The product of two vectors is a vector quantity, then the product is called a dot product.

Q. Explain what is meant by scalar product and vector product.Q. The magnitude of scalar product of two vectors is

8

and of vector product is

8 √ 3

. The angle between them is

Q. The magnitude of scalar product of two vectors is 8 and that of vector product is

8 √ 3

. The angle between them is

View More

स्रोत : byjus.com

## Difference Between Scalar and Vector

Learn about Difference Between Scalar and Vector topic of Physics in details explained by subject experts on vedantu.com. Register free for online tutoring session to clear your doubts

## Difference Between Scalar and Vector

Physics

Difference Between Scalar and ...

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## Scalar and Vector

The two important classifications of a quantity are scalar and vector. The main difference between scalar and vector quantity is that the scalar quantity is the one that is simply related to the magnitude of any quantity. The vector quantity is determined by both the magnitude as well as the direction of the physical quantity.

Considering the dependency on the physical quantities and the direction, they can be classified into two categories – vector and scalar.

The concept of Physics is based on Mathematics. Several concepts and notions that we study in physics mostly rely on Mathematics. Scalar and vector quantities are the two mathematical quantities that explain the motion of a body.

For a common person, the two terms are the same, but there is a huge difference between them in physics. So, have a glance at the information below for your better understanding.

### Definition of Scalar Quantity

The term scalar quantity is defined as a quantity containing only one element in the number field associated with the unit of measurements, such as a degree or meter. It is a quantity that refers only to size or magnitude, that is defined by a numerical value with a measuring unit.

Algebra rules can be applied to link the scalar quantities, like scalars, multiplied, or subtracted similarly as numbers. However, for the scalar quantity, the operation is possible only for the quantities having a similar measurement unit.

### Definition of Vector Quantity

Vector quantity is defined as the mathematical quantity that considers magnitude and direction as two independent characteristics to describe it. Here, magnitude represents the size of the quantity with absolute value. In contrast, direction represents the side i.e., north, east, south, west, north-east, etc.

The triangle law of addition is followed by vector quantity. The vector quantity represented with the help of an arrow placed over or next to the symbol denotes a vector.

### Key Differences Between Scalar and Vector Quantities

The following points are important, so far as the scalar and vector difference is concerned:

The quantity that has magnitude is known as the scalar quantity. Whereas the vector quantity considers both magnitude and direction to describe its physical quantity.

One dimensional quantity can be explained by scalar quantities, for example, a speed of 35 km/h is a scalar quantity. Whereas multidimensional quantities can be described with the help of vector quantities, for example  increase and decrease in temperature.

When there is only a change in the magnitude, the scalar quantity changes, as per the vector quantity, changes in both magnitude and direction are required.

Scalar quantities follow the ordinary algebra rules like addition, multiplication, and subtraction, while vector quantity follows vector algebra rules for performance of operations.

Also, a scalar quantity can divide another scalar quantity, however, two vector quantities cannot be divided.

### Scalar Product of Two Vectors

There are two ways in which vectors can be multiplied - scalar product and vector product.

The scalar of two vectors can be achieved by moving the part of one vector in the other direction and multiplying it times the magnitude of the other vector. The scalar product is also known as inner product or dot product of vectors A and B are shown below:

A·B=|A||B|cos(θ) Where,

| A | is magnitude of vector A,

| B | is magnitude of vector B, and

θ is an angle made by the two vectors

Here, θ is maximum if the direction of motion of an object is along the direction of plane or surface. However, it is zero when an object travels in a direction perpendicular to that of the surface. The outcome of a scalar product of two vectors is a scalar quantity.

For vectors given by their parts: A= (Ax,Ay,Az) and B= (Bx,By,Bz), the scalar product is given by:

A·B = AxBx + AyBy + AzBz

Note that if θ = 90°, then cos(θ) = 0, and therefore we can state that two vectors, with magnitudes not equal to 0, are perpendicular if and only if their scalar product is equal to 0.

The cosine and therefore, the angle between the two vectors can be found with the help of scalar product.

cos(θ)= A.B |A||B| A.B|A||B|

### Properties of Scalar Product

A·B = B·A

A· (B + C) = A·B+ A·C

The value of the angle between two vectors is equal to the scalar product of the vectors divided by the product of their lengths.

If the vectors are perpendicular to each other, then the scalar product is equal to zero.

The scalar product of two vectors is maximum when the vectors are parallel and in the same direction.

If the vectors are antiparallel or in the opposite direction, then the scalar product is minimum.

The self dot product is defined as = A.A. In this product, the angle between the vectors is equal to zero degrees.

The scalar product of orthogonal unit vectors is given as:

i.j = j.k = k.i = 0 as these vectors are perpendicular to each other.

स्रोत : www.vedantu.com

## How to explain the difference between the scalar product and the vector product of two vectors and determine a product in each case

Answer (1 of 3): Dot Product The scalar product is often called the dot product of two vectors. The result of the dot product is a scalar real-valued number. When the vectors are perpendicular, the dot product is zero. Geometrically, the angle \theta between the vectors is 90^{\circ} = \frac{\p...

How do I explain the difference between the scalar product and the vector product of two vectors and determine a product in each case?

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Originally Answered: How do I explain the difference between the scalar product and the vector product of two two vectors and determine a product in each case?

Dot Product

The scalar product is often called the dot product of two vectors. The result of the dot product is a scalar real-valued number.

When the vectors are perpendicular, the dot product is zero. Geometrically, the angle

θ θ

between the vectors is

90 ∘ = π 2 90∘=π2 radians. a ⃗ ∘ b ⃗ = Σ k a k b k =|| a ⃗ ||⋅|| b ⃗ ||cos(θ)

a→∘b→=Σkakbk=||a→||⋅||b→||cos⁡(θ)

a ⃗ ∘ b ⃗ = b ⃗ ∘ a ⃗ a→∘b→=b→∘a→ commutativity result type: scalar

perpendicular result: zero

commutativity means the product is the same in either order

Cross Product

The vector product is often called the cross

Related questions

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What is the scalar and vector product of two vectors?

Evert De Ruiter

PhD in Urban Physiology & Acoustic and Noise Control Engineering, Delft University of Technology (Graduated 2005)Author has 4.4K answers and 799K answer views2y

First thing to realize is, vectors are essentially different from scalars (numbers). There are similarities: you can add or subtract vectors; the result is a vector again. Two other operations are defined on pairs of vectors; one has a vector as a result, the other a scalar. These operations are called vector product and scalar product, after their results. But they are not the same as products of two scalars. They are just defined as they are; however, they are both very useful in physics.

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Satya Parkash Sud

M.Sc. in Physics & Nuclear Physics, University of Delhi (Graduated 1962)Author has 4.7K answers and 13.8M answer viewsAug 3

Related

What is the scalar product of î and -î?

The unit vector i would be written in bold face. Vector i and - i are unit vectors along the x-axis, i being directed along + x-axis and - i is directed along - x-axis ie the vectors are antiparallel to each other (that is the angle between i and - i is 180°.

The scalar product of vectors A and B = |A|.|B| cos( A, B), (where ( A, B ) is the angle between vectors A, B.

Therefore,

i . - i = | i | . | - i | cos 180° = 1 . 1 . -1 = - 1.

Michael Price

MSc in quantum field theoryAuthor has 7.3K answers and 4.1M answer views2y

The scalar product tells you the extent to which two vectors are aligned, and give you a number (or scalar) that represents this amount. If the vectors are parallel the scalar product is the product of the lengths of the two vectors.

The vector product tells you the extent to which two vectors are perpendicular to each other, and gives you a vector that is perpendicular to both.

Deb P. Choudhury

Former Professor at University of AllahabadUpvoted by

David Joyce

, Ph.D. Mathematics, University of Pennsylvania (1979)Author has 8.2K answers and 4.6M answer views4y

Related

What are 2 properties of the scalar product of two vectors?

For any vectors a and b in R^2 or R^3 (In R, it coincides with ordinary multiplication) we define a.b as the real number |a|.|b|.cos(t), where |a| denotes the magnitude or the length or the modulus of a. In general in R^n, if a= (a_1, a_2, ….., a_n), then a.b =(a_1).(a_2)…..(a_n). Two of the important properties of it are:

1 : a.b = b.a for all vectors a and b.

2 : a.(b+c) = (a.b)+(a.c) for all vectors a and b.

3. As a consequence of the definition of the scalar product, it gives the cosine of the angle 't' between the vectors a and b in the form cos(t) = (a.b)/|a|.|b| whenever the vectors are no

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