Channel address:
Categories:
Education
Language: English
Subscribers:
1
Description from channel
Welcome to online library 📕📒📙
📌 Here you will get , Books, DPP, notes, assignment, modules from top coaching institutes 😃
𝐒𝐔𝐏𝐏𝐎𝐑𝐓 & 𝐒𝐇𝐀𝐑𝐄 𝐨𝐮𝐫 𝐜𝐡𝐚𝐧𝐧𝐞𝐥 𝐟𝐨𝐫 𝐦𝐨𝐫𝐞 𝐜𝐨𝐧𝐭𝐞𝐧𝐭
𝓝𝓞 𝓟𝓡𝓞𝓜𝓞𝓢 𝓒𝓞𝓝𝓣𝓔𝓝𝓣 𝓞𝓝𝓛𝓨
Ratings & Reviews
Reviews can be left only by registered users. All reviews are moderated by admins.
5 stars
0
4 stars
3
3 stars
0
2 stars
0
1 stars
0
The latest Messages 8
2021-10-01 18:43:06
Last Date : 10th October hai..to fill NEET Phase-II Registration
50.0K viewsedited 15:43
2021-09-30 07:00:07
Literacy is not just the beginning of education, it's the beginning of a progressive nation! #InternationalLiteracyDay
23.6K views04:00
2021-09-29 18:00:24
Choose the correct answer and comment below
41.4K viewsedited 15:00
2021-09-29 12:30:32
Choose correct option and comment below .
20.2K viewsedited 09:30
2021-09-28 16:41:37
Quiz of the day
42.6K viewsedited 13:41
2021-09-27 18:10:53
40k Members
Thank you...
20.6K viewsedited 15:10
2021-09-27 15:03:21
Quiz of the day
43.1K viewsedited 12:03
2021-09-26 08:30:01
Revision Notes on Vectors
The length or the magnitude of the vector = (a, b, c) is defined by w = √a2+b2+c2
A vector may be divided by its own length to convert it into a unit vector, i.e. ? = u / |u|. (The vectors have been denoted by bold letters.)
If the coordinates of point A are xA, yA, zA and those of point B are xB, yB, zB then the vector connecting point A to point B is given by the vector r, where r = (xB - xA)i + (yB – yA) j + (zB – zA)k , here i, j and k denote the unit vectors along x, y and z axis respectively.
Some key points of vectors:
1) The magnitude of a vector is a scalar quantity
2) Vectors can be multiplied by a scalar. The result is another vector.
3) Suppose c is a scalar and v = (a, b) is a vector, then the scalar multiplication is defined by cv = c (a, b) = (ca, cb). Hence each component of vector is multiplied by the scalar.
4) If two vectors are of the same dimension then they can be added or subtracted from each other. The result is gain a vector.
If u, v and w are three vectors and c, d are scalars then the following results of vector addition hold true:
1) u + v = v + u (the commutative law of addition)
2) u + 0 = u
3) u + (-u) = 0 (existence of additive inverses)
4) c (du) = (cd)u
5) (c + d)u = cu + d u
6) c(u + v) = cu + cv
7) 1u = u
8) u + (v + w) = (u + v) + w (the associative law of addition)
Some Basic Rules of Algebra of Vectors:
1) a.a = |a|2 = a2
2) a.b = b.a
3) a.0 = 0
4) a.b = (a cos q)b = (projection of a on b)b = (projection of b on a) a
5) a.(b + c) = a.b + a.c (This is also termed as the distributive law)
6) (la).(mb) = lm (a.b)
7) (a ± b)2 = (a ± b) . (a ± b) = a2 + b2 ± 2a.b
8) If a and b are non-zero, then the angle between them is given by cos θ = a.b/|a||b|
9) a x a = 0
10) a x b = - (b x a)
11) a x (b + c) = a x b + a x c
Any vector perpendicular to the plane of a and b is l(a x b) where l is a real number.
Unit vector perpendicular to a and b is ± (a x b)/ |a x b|
The position of dot and cross can be interchanged without altering the product. Hence it is also represented by [a b c]
1) [a b c] = [b c a] = [c a b]
2) [a b c] = - [b a c]
3) [ka b c] = k[a b c]
4) [a+b c d] = [a c d] + [b c d]
5) a x (b x c) = (a x b) x c, if some or all of a, b and c are zero vectors or a and c are collinear.
Methods to prove collinearity of vectors:
1) Two vectors a and b are said to be collinear if there exists k ? R such that a = kb.
2) If p x q = 0, then p and q are collinear.
3) Three points A(a), B(b) and C(c) are collinear if there exists k ? R such that AB = kBC i.e. b-a = k (c-b).
4) If (b-a) x (c-b) = 0, then A, B and C are collinear.
5) A(a), B(b) and C(c) are collinear if there exists scalars l, m and n (not all zero) such that la + mb+ nc = 0, where l + m + n = o
Three vectors p, q and r are coplanar if there exists l, m ? R such that r = lp + mq i.e., one can be expressed as a linear combination of the other two.
If [p q r] = 0, then p, q and r are coplanar.
Four points A(a), B(b), C(c) and D(d) lie in the same plane if there exist l, m ? R such that b-a = l(c-b) + m(d-c).
If [b-a c-b d-c] = 0 then A, B, C, D are coplanar.
Two lines in space can be parallel, intersecting or neither (called skew lines). Let r = a1 + μb1 and r = a2 + μb2 be two lines.
They intersect if (b1 x b2)(a2 - a1) = 0
The two lines are parallel if b1 and b2 are collinear.
The angle between two planes is the angle between their normal unit vectors i.e. cos q = n1 . n2
If a, b and c are three coplanar vectors, then the system of vectors a', b' and c' is said to be the reciprocal system of vectors if aa' = bb' = cc' = 1 where a' = (b xc) /[a b c] , b' = (c xa)/ [a b c] and c' = (a x b)/[a b c] Also, [a' b' c'] = 1/ [a b c]
Dot Product of two vectors a and b defined by a = [a1, a2, ..., an] and b = [b1, b2, ..., bn] is given by a1b1 + a2b2 + ..., + anbn .
38.0K views05:30
2021-09-25 05:41:14
Choose the correct answer
26.6K viewsedited 02:41
2021-09-24 17:20:12
Notes on Chemical Coordination and Regulation
Properties of hormones
(a) These are secreted by endocrine gland (biogenic in origin).
(b) Their secretions is released directly into blood (except local hormones e.g. gastrin).
(c) These are carried to distantly locate specific organs, called target organ.
(d) These have specific physiological action (excitatory or inhibatory). These co-ordinate different physical, mental and metabolic activities and maintain homeostasis.
(e) The hormones have low molecular weight e.g. ADH has a molecular weight of 600–2000 daltons.
(f) These act in very low concentration e.g. around10–10 molar.
(g) Hormones are non antigenic.
(h) These are mostly short-lived. So have a no camulative effect.
(i) Some hormones are quick acting e.g. adrenalin, while some acting slowly e.g. ostrogen of ovary.
(j) Some hormones secreted in inactive form called Prohormone e.g. Pro-insulin.
(k) Hormones are specific. They are carriers of specific information to their specific target organ. Only those target cell respond to a particular hormone for which they have receptors.
@arvind_arora_vedantu_chemistry
42.3K views14:20
ᅠ
