Two vectors have magnitude 2 m and 3 m. The angle between them is 60°. Find a) the scalar product of two vector. b) magnitude of their vector product.

-

Ans: Consider two vectors a and b.

Given : | 𝑎 | = 2m and 

| 𝑏 | = 3m 

Angle between vector a and vector b is 60°, say θ = 60°

(a) Scalar product:

a.b = |a| |b| cos θ

= 2 x 3 x cos 60°

= 6 x 1/2

= 3 m²

(b) magnitude of vector product:

|a x b| = |a| |b| sin θ

= 2 x 3 x sin 60°

= 6 x √3/2

= 3√3 m²

Comments

Post a Comment

Popular posts from this blog

Diagonal Relationship between Beryllium and Aluminium || Relation between Beryllium and Aluminium

-
  Diagonal Relationship between Beryllium and Aluminium The ionic radius of Beryllium (Be 2+) is estimated to be nearly 31 pm; the charge/radius ratio Or e/m ratio is nearly the same as that of the Al 3+ ion. Hence beryllium resembles aluminium in these ways. Some of the similarities are given below: » Like Aluminium, Beryllium(be) is not readily attacked by acids H+ donor because of the formation of an oxide film on the surface of the metal by reacting with oxygen, i.e. they are rendered passive by nitric acid. » Beryllium hydroxide[[Be(OH)4]2] dissolves in excess of alkali to give a beryllate ion, [ Be(OH)4]2– just as aluminium hydroxide[Al(OH)3] gives aluminate ion, [Al(OH)4] » The chlorides of metals beryllium and aluminium have Cl– bridged chloride structure in vapour phase. Both the chlorides are soluble in organic solvents and are strong as Lewis acids They are used as Friedel Craft catalysts. » Beryllium(Be) and aluminium(Al) ions have strong tendency to form complexes, (BeF4)2
Read more

KVS CBSE Worksheets CHAPTER 1 Electric Charges and Fields Class 12

-
Image
                      SECTION A CONCEPTUAL AND APPLICATION TYPE QUESTIONS  1 Is the force acting between two point charges q1 and q2 kept at some distance apart in air attractive or repulsive when i) q1 q2 > 0 ii) q1 q2 < 0 ? 1 (2007)  2 If the distance between two equal point charges is doubled and their individual charges are also doubled ,what would happen to the force between them ? 1(2014)  3 Do the electrostatic field lines form closed loops? 1(2014)  4 A hollow metal sphere of radius 5cm is charged such that the potential on its is 10V. What is the electric field at the center of the sphere? 1(2011)  5 What is meant by the statement that   “the electric field of a point charge has spherical symmetry whereas electric field due to an electric dipole is cylindrically symmetrical’’ ? 1(1996)  6 Why is it difficult to perform electrostatic experiments on a humid day? 1  7 The distance of the field point on the equatorial plane of a small electric dipole , is halved. By wha
Read more

S-Block Elements || S-block element class 11 chapter 8 || Group 1A, 2A elements || S block elements chapter 8 notes class 11 || Chemistry ||

-
Image
                    INTRODUCTION : The s- block elements of the periodic table are those in which the last electron enters  into the outermost s-orbital. As the s-orbital can accommodate only two electrons, in two group (1 & 2) belong to the s-block of the periodic table. Group 1 of the periodic table consists of the elements : lithium (L i), sodium (Na), potassium (K), rubidium (R b), caesium (C s) and francium (F r). They are collectively known as alkali metals. These are called because they forms hydroxides on reaction with water which are strongly alkaline in nature. The elements of Group 2nd include beryllium (Be), magnesium (Mg), calcium (C a), strontium (S r), barium (B a) and radium (Ra). These elements with the exception of Beryllium are commonly known as the alkaline earth metals. These are so called because their oxide and hydroxide are alkaline in nature and these metal oxides are found in the earth’s crust . The general electronic configuration of s- block element is
Read more

Electric Charges and Fields || Electrostatics Notes || Physics || Class 12 || Chapter 1 Notes Class 12 ||

-
Image
                            Charge Charge is that property of an object by virtue of which it apply electrostatic force of interaction on other objects. Charges are of two types (i) Positive charge (+ve)  (ii) Negative charge (-ve)  Like charges repel and unlike charges attract each other.               Quantization of Charge Charge on any object can be an integer multiple of a smallest charge (e).                     Q = ± n e where, n = 1, 2, 3,……. and e = 1.6 * 10-19 C.                   Conservation of Charge Charge can neither be created nor be destroyed. but can be transferral from one object to another object. Recently a new particle has been discovered called ‘Quark’. It contains charge ± e / 3, ± 2e / 3. [The protons and neutrons are combination of other entities called quarks, which have charges 1 / 3 e. However, isolated quarks have not been observed, so, quantum of charge is still e. ]         Coulomb’s Law of Electrostatics Electrostatic force of interaction acting betwee
Read more

Diwali 2020 || Deepawali 2020 || Happy diwali || Festival of lights || 2020 ||

-
Image
                            Diwali Diwali is the festival of lights. Diwali is one of the most popular festivals of Hindus all over the world which is celebrated with great excitement , happiness and delight. Kids have a great time on Diwali as they get an opportunity to share their joyful experiences about the festival. Youngsters usually love this festival as it brings a lot of happiness and delightful moments for everyone. They get to meet their family, friends and relatives and share greetings and gifts with their loved ones. Diwali is also popularly known as “Deepawali” is one of the most celebrated festivals of Hindus residing in India or across the world. Diwali is celebrated with great fervour and enthusiasm by people throughout the world. Although it’s considered as a Hindu festival, but people from different communities celebrate the bright festival by bursting crackers and fireworks. According to Hindu mythology, Diwali is a festival which commemorates the return of Lord Ram
Read more