🔥Revision Notes on Vectors
Some Basic Results of Vector Calculus:
1) Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.
2) Column vectors can be added by simply adding the values in each row.
3) You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.
4) If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2
5) Collinear Vectors are also parallel vectors except that they lie on the same line.
6) When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.
7)Two collinear vectors are always linearly dependent.
8) Two non-collinear non-zero vectors are always linearly independent
9) Three coplanar vectors are always linearly dependent.
10) Three non-coplanar non-zero vectors are always linearly independent
11) More than 3 vectors are always linearly dependent.
12) Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.
Some Basic Results of Vector Calculus:
1) Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.
2) Column vectors can be added by simply adding the values in each row.
3) You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.
4) If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2
5) Collinear Vectors are also parallel vectors except that they lie on the same line.
6) When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.
7)Two collinear vectors are always linearly dependent.
8) Two non-collinear non-zero vectors are always linearly independent
9) Three coplanar vectors are always linearly dependent.
10) Three non-coplanar non-zero vectors are always linearly independent
11) More than 3 vectors are always linearly dependent.
12) Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.
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Forwarded from HORROR
The range of the function f(x) = tan(Root)x²/9 - x² is
Anonymous Quiz
21%
A] (0, 3 )
43%
B] ( 3 , root 3 )
26%
C] (0, root3 )
9%
D] (root 3 , 3)
👍6❤3🥰3👏3🔥2😁2
Forwarded from HORROR
[💀] The number of unpaired electrons in the gaseous ions
Mn³+ , Cr³+ , V³+ and Ti³+ are
respectively :
Mn³+ , Cr³+ , V³+ and Ti³+ are
respectively :
Anonymous Quiz
24%
A) 3 , 2 , 3 and 1
33%
B) 2, 2 , 3 and 1
29%
C) 4 , 3 , 2 and 1
15%
D) 1 , 2 , 3 and 4
👍8❤2🔥2👏1
Forwarded from HORROR
The locus of mid point of the chord of contact of tangents drawn from points lying on the straight line
4x - 5y = 20 to the circle X² + Y² = 9 is
4x - 5y = 20 to the circle X² + Y² = 9 is
Anonymous Quiz
19%
A] 20 (x² + y² ) - 36x - 45y = 0
27%
B] 20 (x² + y² ) + 36x - 45y = 0
31%
C] 36 ( x² + y² ) - 20x + 45y = 0
15%
D] 36 ( x² + y² ) + 20x - 45y = 0
7%
E] 20 (x² + y² ) - 36x + 45y = 0
😱10👍7❤6🔥3🥰3🤩2👏1
✅Genetic Terminology
▪️ Allele➖An alternative form of a gene
▪️ morph➖A silent gene
▪️ Angelman syndrome➖a rare genetically inherited form of mental retardation
▪️ Autosome➖Synonymous with somatic chromosomes
▪️ Chimera➖An exceptionally rare person composed of the cells derived from different zygotes
▪️ Chromosome➖Rod-shaped or thread-like structures located within the cell nucleus that carry genes encoded by DNA
▪️ Cloned gene➖A recombinant DNA molecule along with the gene of interest
▪️ Consanguinity➖Having a common ancestor, i.e., blood relations
▪️ Crossing over➖The exchange of genetic material between a pair of homologous chromosomes
▪️ Cross-pollination➖Mating of two genetically different plants (but of the same species).
▪️ Dizygotic twins➖Twins produced from two separate ova, which are separately fertilized
▪️ Deoxyribonucleic acid (DNA)➖Composed of nucleic acids, DNA encodes the genes that facilitate genetic information to be passed to offspring.
▪️ Evolution➖Genetic change in a population of organisms over period of time
▪️ Gamete➖A reproductive sex cell (i.e. ovum or sperm)
▪️ Gene➖Units of inheritance typically occurring at specific locations (a chromosome)
▪️ Gene Pool➖All of the genes in all of the individuals in a breeding population
▪️ Gene Flow➖The transference of genes from one population to another
▪️ Genetic Drift➖Evolution, or change in gene pool frequencies, resulting from a random chance
▪️ Genetics➖Study of gene structure, action, and the patterns of inheritance of traits from parent to offspring
▪️ Genome➖The full genetic complement of a species
▪️ Genomic imprinting➖The epigenetic phenomenon by which certain genes are expressed in a parent-of-origin-specific manner
▪️ Genotype➖Genetic constitution of a cell (of an individual organism)
▪️ Gout➖Genetically inherited metabolic disorder (or a type of arthritis)
▪️ Hemophilia➖Genetic disorder (largely inherited), problem in blood clotting
▪️ Heterozygous➖A cell containing two different alleles of a gene
▪️ Huntington's disease➖An inherited disorder that results into death of brain cells
▪️ Hybrid➖Combining the qualities of two animals or plants of different breeds, varieties, species (also known as crossbreed)
▪️ Mutation➖Change that occurs in DNA sequence
▪️ Pleiotropy➖When one gene influences two or more apparently unrelated phenotypic traits
▪️ Psoriasis➖ An inherited disease categorized by recurring thick, reddish patches on skin
▪️ Syntenic➖Genes occurring on the same chromosome
▪️ Zygote➖The fertilized egg is known as zygote
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▪️ Allele➖An alternative form of a gene
▪️ morph➖A silent gene
▪️ Angelman syndrome➖a rare genetically inherited form of mental retardation
▪️ Autosome➖Synonymous with somatic chromosomes
▪️ Chimera➖An exceptionally rare person composed of the cells derived from different zygotes
▪️ Chromosome➖Rod-shaped or thread-like structures located within the cell nucleus that carry genes encoded by DNA
▪️ Cloned gene➖A recombinant DNA molecule along with the gene of interest
▪️ Consanguinity➖Having a common ancestor, i.e., blood relations
▪️ Crossing over➖The exchange of genetic material between a pair of homologous chromosomes
▪️ Cross-pollination➖Mating of two genetically different plants (but of the same species).
▪️ Dizygotic twins➖Twins produced from two separate ova, which are separately fertilized
▪️ Deoxyribonucleic acid (DNA)➖Composed of nucleic acids, DNA encodes the genes that facilitate genetic information to be passed to offspring.
▪️ Evolution➖Genetic change in a population of organisms over period of time
▪️ Gamete➖A reproductive sex cell (i.e. ovum or sperm)
▪️ Gene➖Units of inheritance typically occurring at specific locations (a chromosome)
▪️ Gene Pool➖All of the genes in all of the individuals in a breeding population
▪️ Gene Flow➖The transference of genes from one population to another
▪️ Genetic Drift➖Evolution, or change in gene pool frequencies, resulting from a random chance
▪️ Genetics➖Study of gene structure, action, and the patterns of inheritance of traits from parent to offspring
▪️ Genome➖The full genetic complement of a species
▪️ Genomic imprinting➖The epigenetic phenomenon by which certain genes are expressed in a parent-of-origin-specific manner
▪️ Genotype➖Genetic constitution of a cell (of an individual organism)
▪️ Gout➖Genetically inherited metabolic disorder (or a type of arthritis)
▪️ Hemophilia➖Genetic disorder (largely inherited), problem in blood clotting
▪️ Heterozygous➖A cell containing two different alleles of a gene
▪️ Huntington's disease➖An inherited disorder that results into death of brain cells
▪️ Hybrid➖Combining the qualities of two animals or plants of different breeds, varieties, species (also known as crossbreed)
▪️ Mutation➖Change that occurs in DNA sequence
▪️ Pleiotropy➖When one gene influences two or more apparently unrelated phenotypic traits
▪️ Psoriasis➖ An inherited disease categorized by recurring thick, reddish patches on skin
▪️ Syntenic➖Genes occurring on the same chromosome
▪️ Zygote➖The fertilized egg is known as zygote
|| IF YOU LIKE IT
GIVE REACTIONS ❤️||
👍24❤12🥰7
Forwarded from HORROR
Oxidation number (s) of potassium in K2O , K2O2 and KO2 , respectively , is ( are ) ______
Anonymous Quiz
32%
A] +2 , +1 And + 1/2
39%
B] +1 , +2 and +4
20%
C] +1 , +4 and +2
9%
D] +1 , +1 and +1
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Forwarded from HORROR
The area bounded by the curve x = 2 - y - y² and the Y-axis is
Anonymous Quiz
19%
A] 9/2 sq. units
24%
B] 5/2 sq. units
27%
C] 7/2 sq. units
17%
D] 11/2 sq. units
13%
E] 10/2 sq. units
👍9👌7❤3😱1
Forwarded from HORROR
The number of orbitals associated with quantum number n = 5 , ms = +1/2 is _______
Anonymous Quiz
31%
A] 20
31%
B] 24
26%
C] 15
13%
D] 25
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Forwarded from HORROR
Identify the one which is not a disorder of the circulatory system .
Anonymous Quiz
25%
A] Emphysema
36%
B] Coronary artery disease
27%
C] Angina pectoris
13%
D] Myocardial infarction
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Forwarded from HORROR
The units of surface tension and viscosity of liquids are respectively __________
Anonymous Quiz
43%
A] N m-¹ , kg m-¹ s-²
30%
B] kg m-¹s-¹ , N m-¹
19%
C] kg s-² , kg m-¹
8%
D] kg s-¹ , kg m-²
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Forwarded from HORROR
The isomer of C4H9I which is capable of producing but-2-ene with alc. KOH solution is _______ .
Anonymous Quiz
18%
A] 1- iodobutane
42%
B] 1- iodo-2- methylpropane
29%
C] 2-iodobutane
11%
D] 2- iodo-2- methylpropane
👍7🥰5🔥3🤩3❤1🤔1
Forwarded from HORROR
The copolymer obtained on condensation reaction between glycine and *-aminocarproic acid is ________
Anonymous Quiz
27%
A] Glyptal
36%
B] Nylon 6 ,6
29%
C] Nylon 2-nylon 6
8%
D] PHBV
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👍20
Forwarded from HORROR
The reaction take place in two steps as
1) NO2Cl -------k1--------> NO2 + Cl 2) NO2Cl + Cl -------k2------> NO2 + Cl Identify the reaction intermidate
1) NO2Cl -------k1--------> NO2 + Cl 2) NO2Cl + Cl -------k2------> NO2 + Cl Identify the reaction intermidate
Anonymous Quiz
22%
A] Cl
21%
B] NO2
38%
C] NO2Cl
13%
D] Cl2
6%
E] CO2
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Forwarded from HORROR
Identify organometallic compounds .
Anonymous Quiz
31%
A] CH3Mgl
27%
B] CH3ONa
17%
C] C2H5SNa
25%
D] All of these 🙁
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Forwarded from .
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Then Join below and choose your target
👍6🤔4
Forwarded from HORROR
Aqueous solution of which of the following compounds is the best conductor of electric current ?
Anonymous Quiz
33%
A] Hydrochloric acid, HCl
21%
B] Ammonia , NH3
16%
C] Fructose , C6H12O6
12%
D] Acetic acid , C2H4O2
18%
E] All of these
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