fi Vector fi ivwk Vector Quantities h m

‡f±i ivwk (Vector Quantities): ‡h m. Kj †fŠZ ivwk‡K m¤ú~Y©iƒ‡c cÖKvk Kivi Rb¨ gvb

‡¯‹jvi ivwk (Scalar Quantities): ‡h m. Kj †fŠZ ivwk‡K ïay gvb Øviv m¤ú~Y©iƒ‡c cÖKvk

mw. VK †f±i (Restricted Vector): ‡h m. Kj †f±‡ii gvb k~Y¨ bq Zv‡`i‡K mw.

‡f±i ivwki †hv. M Kivi wbqg: 1| wÎf‚R m~Î 2| eûf‚R m~Î 3| mvgšÍwi‡Ki

GKB we›`y‡Z wµqvkxj `yw. U mgvb gv‡bi †f±‡ii ga¨e. Z©x †Kv. Y KZ n‡j

1| GKw. U b`x‡Z †¯ªv‡Zi †e. M 2 kmh-1 Ges †¯ªv. Znxb -1 kmh

b`x‡Z GKw. U †bŠKvi †e. M †¯ªv‡Zi Aby. K‚‡j 18 kmh-1 -1 Ges cÖw.

‡f±i wefv. Rb ev †f±i we‡kølb (Resolution Of Vectors) t GKw. U †f±i ivwk‡K

‡¯‹jvi ‡ÿÎ (Scalar field): †Kvb ¯’v‡bi †Kvb Gjv. Kv ev A ‡ji cÖw. Zw.

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‡f±i (Vector)

‡f±i ivwk (Vector Quantities): ‡h m. Kj †fŠZ ivwk‡K m¤ú~Y©iƒ‡c cÖKvk Kivi Rb¨ gvb I w`K Df‡qi cÖ‡qv. Rb nq Zv‡`i‡K ‡f±i ivwk e‡j| †hgb- mi. Y, IRb, †e. M, Z¡i. Y, ej BZ¨vw`|

‡¯‹jvi ivwk (Scalar Quantities): ‡h m. Kj †fŠZ ivwk‡K ïay gvb Øviv m¤ú~Y©iƒ‡c cÖKvk Kiv hvq Zv‡`i‡K ‡¯‹jvi ivwk e‡j| †hgb- `yªw. Z, fi, Kv. R, ‰`N©¨ BZ¨vw`|

O B

mw. VK †f±i (Restricted Vector): ‡h m. Kj †f±‡ii gvb k~Y¨ bq Zv‡`i‡K mw. VK †f±i e‡j| bvj ev k~Y¨ †f±i : ‡h †f±‡ii gvb k~Y¨ Zv‡K bvj ev k~Y¨ †f±i e‡j| wecÖZxc †f±i : `yw. U mgvšÍivj †f±‡ii GKw. Ui gvb Acw. Ui wecix. Z ms. L¨v n‡j Zv‡`i‡K wecÖZxc †f±i e‡j|

Y P O X

Y O Z X

‡f±i ivwki †hv. M

‡f±i ivwki †hv. M Kivi wbqg: 1| wÎf‚R m~Î 2| eûf‚R m~Î 3| mvgšÍwi‡Ki m~Î

C A B

B O C A

C O B A N

C O B A N

GKB we›`y‡Z wµqvkxj `yw. U mgvb gv‡bi †f±‡ii ga¨e. Z©x †Kv. Y KZ n‡j G‡`i jwäi gvb †h †Kvb GKw. U †f±‡ii mgvb n‡e?

1| GKw. U b`x‡Z †¯ªv‡Zi †e. M 2 kmh-1 Ges †¯ªv. Znxb -1 kmh b`x‡Z GKRb mvu. Zviy 4 †e‡M mvu. Zvi Kv. U‡Z cv‡ib| mvu. Zviy‡K b`xi GK cÖvšÍ ‡_‡K †mv. Rv Aci cÖv‡šÍ †h‡Z †Kvb w`‡K KZ †e‡M hvÎv Ki‡Z n‡e? 2| hw` b`xi cÖ¯’ 1 km nq Z‡e b`x cvi n‡Z KZ mgq jv. M‡e ?

b`x‡Z GKw. U †bŠKvi †e. M †¯ªv‡Zi Aby. K‚‡j 18 kmh-1 -1 Ges cÖw. ZK‚‡j 6 kmh | †bŠKvw. U †Kvb w`‡K Pvjbv Ki‡j †mv. Rv Aci cv‡o †cŠu. Qv‡e Ges ZLb †bŠKvi †e. M KZ n‡e ?

Ae¯’vb †f±i

Y P(x, y, z) A B Z X O N

†f±i ivwki ¸Yb

N O B M A

‡f±i wefv. Rb

‡f±i wefv. Rb ev †f±i we‡kølb (Resolution Of Vectors) t GKw. U †f±i ivwk‡K `y. B ev Z‡Zvwa. K †f±i ivwk‡Z wef³ Kivi c×w. Z‡K †f±‡ii wefv. Rb ev †f±‡ii we‡kølb e‡j| B O C A

B O C A

‡f±i K¨vj. Kzjvm

‡¯‹jvi ‡ÿÎ (Scalar field): †Kvb ¯’v‡bi †Kvb Gjv. Kv ev A ‡ji cÖw. Zw. U we›`y‡Z hw` GKw. U †¯‹jvi ivwk we`¨gvb _v‡K , Z‡e H A j‡K H ivwki †¯‹jvi †ÿÎ e‡j| ‡f±i †ÿÎ (Vector field): †Kvb ¯’v‡bi †Kvb Gjv. Kv ev A ‡ji cÖw. Zw. U we›`y‡Z hw` GKw. U ‡f±i ivwk we`¨gvb _v‡K , Z‡e H A j‡K H ivwki ‡f±i †ÿÎ e‡j| Acv‡i. Ui (Operator): †h Mvw. Yw. ZK w. Pý GKw. U ivwk‡K Ab¨ GKw. U ivwk‡Z i~cvšÍwi. Z K‡i Zv‡K Acv‡i. Ui e‡j|