Scalar & Vector product of three & four vector .

Scalar & Vector product of three & four vector, Change of variables , Gradient ,Divergence & Curl.
Paper Name - Vector Analysis & Geometry
Paper No - III
Unit - I
Shri shankaracharya mahavidyalaya junwani bhilai .

1. Shy? Shankatachanya MahaVdNoya , Suawei
BK lot 3 ~
Sobfect:- Vector Analysts and heared
pare” (ID)

ae
Une ~L

2. Scalar tuple and Far tr Luzern
albu) ar labt jer labscl.— >

Ve fie product ER RE EE

if er í ettor
ax hxc).

Um Galan I 510
eS = Euer soa

+ | scan product of hs == ES commu
y es OO Ena en
Tae had) se + Caxh) = Chad) 87 a!

he cuelte. order of the actors tan be 1 he changed

IT mal ine sign. is changed

RE LUE fe AA AAA A
- ar Are

aan ma]

| The. scala hf ple_precluad_ot wit wech, ERS
wi Hep. ES kay.

3. — : a
— Remember, 2
| is Jef eee Se
(ee: Sule =
Ï

LL TA Phe vel £ ax (bac) whey
Le Gs feos tk Bos atest’, :

| ® = I a2, =
[Here bx ©. | X 1 2]
af

P= Cs -2)F + Gey + [4-
= 314 34 5K

1
Lox@mye): Ji 3

È

_ À

I 1-3 3
1 SETESTETEESHE TERN
1 = 91-6) -3k Am. hi y

Mel Pind the value af Ce. 8
¡ueno aa = Dx, R =>
Ze 2) P = BJ —M

ers,
= 2th 2) =

Lee)

D'b 3 CzaitjtWs
= ASEO

ESE Gf +h)

ae
Fr

4. On q

i | ee ET
ara AA RI

AR
Al Scalar Punduch ot Faux Vector (RAR
sta wear)

al

ed) [are aed | —

“lise va)
Eur _ _
lie ad a a 2
añ oh

[fbedla=facddbt fabdyc- fabald =

el era ot Rec protal _ y E of vechre- |

Í 1 ran wena à UT

í j :

rc a na
LAA A A
[ fase] fève) nr

whee O ame non —toblanas ve y
PS al APRA —]

YO ts called necipretal_ system oF the

o J

5. sek of vechvs, À 1b)

®
a.@ı=l PL, Pers]

aS | Puoperhy. I! -
IE

DL pri De à

N

Di Esopeity DET = The equation af GE, can

=. [rrelo + [Pealr free
| fe Re? for Ol [PP Pe)

NAVE + Cy yet ASA

cag?

+ u Ys
a BEAN

Fl Diffouont hen of Vectors CU

Eom

| TT ote

Clas oF vecinr function! =

Lin PH:

4> to

6. + bY
LA
Cantal = =

7 y &

Al digit He)

4 45

— + | Rome Empontdant Ro uH1-

1 ON je MAA tet Dae FY

einen ee HT

La ee PETE du Pe O

LG Fa ob [ale FT Y

ise BEG Eta ef pe

fae Pet Wie D
rane ES es Be N

Bert Zee

E24
eI Th a2sing; + ts Qs ye be 050% sn

i?
clk, Pad 08j-3k,—|

dE NEO ARE —

En)

de > ti BS +k

7. - i Fu
Cese She > |
= EE | A
2 Catsing) f+ les0-0) 5 4 Brasa 15h)

[lud de OO tor] erp tordo)

= Coogi sins th) Eg asia —

SL ja Geese Ds
MEA

ee
RER a _

35)x bats 3} —

(Loge she). E
Cane_a2f when 6 D.

— test sin,
==] = ÍA IO chen
<a thus ax [dy xe jac
A A 2
ba axfhx des o

_ I now eohrrallag O, =
cere heey y. 7} Ej CR hen 620
de

8. AA

Had ont quel -Divesgen e

x

br yadiont af a scala paint Euntilon
way Re her a fret)

Awad = de Por dis quad I
n

Aa Y > vector dunch'on

EAS

The: opelta lor E

pl
sia $ |
Juda Di 4 UP pe NÉ 5

Ez =a fe ds ]

EAS ECO = 4

Po A = i
Ve AA 2

aude gp) —
| To empres the cle ho, vata + |

foyadiont eft canskınt. Gas “a PART)

Judo TR 1529 KE

mudado

9. ad dv À
have. div à

10. 3 3 ety be?

y E

CUR oF vector Cód)

RE ii a |

Api yz,

er a prox par)
Y

5 E E) i
= cl E
Hente Curl F > YX. A
SA 4 IE
Pia EY ay tz.

But Vik x pled

- E
Expression of cub E In tom oP companend of Fo

META

i me
Ea EY ES
po Py et