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Class 10 Class 12

સદિશનું બીજગણિત

નીચેના સદિશનું માન શોધો :
$open parentheses 2 comma space 3 comma space square root of 3 close parentheses$

નીચેના સદિશનું માન શોધો :
$3 space straight i with hat on top space minus space 4 straight k with hat on top$

2 straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top

ની દિશામાં એકમ સદિશ શોધો.

20 માનવાળો અને $negative 3 straight i with hat on top space plus space 2 square root of 3 space straight j with hat on top space minus space 2 straight k with hat on top$ ની દિશાની વિરુદ્ધ દિશાનો સદિશ શોધો.

અહીં, $stack straight x space with bar on top space equals space minus 3 straight i with hat on top space plus space 2 square root of 3 space straight j with hat on top space minus space 2 straight k with hat on top space equals space open parentheses negative 3 comma space 2 square root of 3 comma space minus 2 close parentheses$

$therefore space open vertical bar space stack straight x space with bar on top close vertical bar space equals space square root of open parentheses negative 3 close parentheses squared space plus space open parentheses 2 square root of 3 close parentheses squared space plus space open parentheses negative 2 close parentheses squared end root space space space space space space space space space space equals space square root of 9 space plus space 12 space plus space 4 end root space equals space square root of 25 space equals space 5$

$therefore space stack straight x space with bar on top space equals space open parentheses negative 3 comma space 2 square root of 3 comma space minus 2 close parentheses$ ની દિશાની વિરુદ્ધ દિશામાં 20 માનવાળો સદિશ

$equals thin space fraction numerator negative 20 space straight x with bar on top over denominator open vertical bar straight x with bar on top close vertical bar end fraction space equals space fraction numerator negative 20 space open parentheses negative 3 comma space 2 square root of 3 comma space minus 2 close parentheses over denominator 5 end fraction equals space open parentheses 12 comma space minus 8 square root of 3 comma space 8 close parentheses space equals space bold 12 bold i with bold hat on top bold space bold minus bold space bold 8 square root of bold 3 bold j with bold hat on top bold space bold plus bold space bold 8 bold k with bold hat on top$

$stack straight x space with bar on top space equals space 3 straight i with hat on top space plus space 4 straight j with hat on top space minus space 5 straight k with hat on top space space bold અન ે bold space space stack straight y space with bar on top space equals space 2 straight i with hat on top space plus space straight j with hat on top comma$ , સદિશો માટે $stack straight x space with bar on top space plus space 2 stack space straight y space with bar on top$ ની દિશામાં એકમ સદિશ મેળવો.

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સદિશનું બીજગણિત

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